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Longer titles found: Stable homotopy theory (view), Rational homotopy theory (view), Weak equivalence (homotopy theory) (view), A¹ homotopy theory (view), Coherency (homotopy theory) (view), Chromatic homotopy theory (view), Simple homotopy theory (view), Equivariant stable homotopy theory (view)

searching for Homotopy theory 153 found (510 total)

alternate case: homotopy theory

Andreotti–Frankel theorem (251 words) [view diff] no match in snippet view article find links to article

In mathematics, the Andreotti–Frankel theorem, introduced by Aldo Andreotti and Theodore Frankel (1959), states that if V {\displaystyle V} is a smooth

and provides natural settings for intersection theory (or motivic homotopy theory) of singular algebraic varieties and cotangent complexes in deformation

localization and completion in homotopy theory, and in the study of homotopy properties of schemes (e.g. étale homotopy theory). Edwards, David A.; Hastings

contributions to algebraic topology, particularly equivariant stable homotopy theory, algebraic K-theory, and applied algebraic topology". In 2008, Carlsson

professor at Amherst College. He studies, among other things, étale homotopy theory, elliptic surfaces, computer-based algebraic geometry (such as Gröbner

group is important because of its relation to Galois theory, étale homotopy theory, and the ring of adeles. In addition, it provides a basic tractable

pro-simplicial set associated to the étale topos of a scheme is called étale homotopy theory. In good cases (if the scheme is Noetherian and geometrically unibranch)

at an early stage of their career. The prize is named in memory of homotopy theory pioneer J. H. C. Whitehead. More specifically, people being considered

in 1952, with a thesis titled Abstract Function Spaces and Their Homotopy Theory. All of these degrees were from UCLA where Jackson remained in the

and Russian mathematician known for his work on algebraic topology, homotopy theory, and mathematical physics. Buchstaber's first research work was in

Technology, under the supervision of Daniel Quillen, with thesis Abstract Homotopy Theory and Generalized Sheaf Cohomology. Hired by Cornell University in 1971

simplicial commutative ring from the point of view of homotopy theory? W. G. Dwyer and D. M. Kan. “Homotopy theory and simplicial groupoids”. In: Nederl. Akad.

Deligne, Phillip Griffiths, John Morgan, and Dennis Sullivan. Real homotopy theory of Kähler manifolds. Invent. Math. 29 (1975), no. 3, 245–274. MR0382702

Novikov. Morava K-theory Michael J. Hopkins, Global methods in homotopy theory, in Homotopy theory (Durham, 1985), 73–96, London Math. Soc. Lecture Note Ser

Nice, and in 1995 at the University of Lille. His research deals with homotopy theory and homology of loop spaces with applications in geometry. He wrote

mathematician, known for his work in algebraic topology, especially homotopy theory. Ganea left Communist Romania to settle in the United States in the

mathematician specializing in topology, including algebraic topology, homotopy theory, and geometric topology. She is a professor of mathematics at the University

mathematics at the University of Manchester. Eccles specialises in homotopy theory and its applications to different topology. Eccles taught a wide variety

(∞, 1)-categories. Rezk, Charles (2001), "A model for the homotopy theory of homotopy theory", Transactions of the American Mathematical Society, 353 (3):

0043. S2CID 168002. Rezk, Charles (2001). "A model for the homotopy theory of homotopy theory". Transactions of the American Mathematical Society. 353 (3):

rest of his career. Cohen did influential work in several areas of homotopy theory. His thesis concerned the topology of configuration spaces, a topic

of Edgar H. Brown, Jr. His thesis was titled On Odd Primary Stable Homotopy Theory. He did his postdoctoral training as an L.E. Dickson Instructor at

This is a timeline of bordism, a topological theory based on the concept of the boundary of a manifold. For context see timeline of manifolds. Jean Dieudonné

Pierre; Griffiths, Phillip; Morgan, John; Sullivan, Dennis (1975). "Real homotopy theory of Kähler manifolds". Inventiones Mathematicae. 29 (3): 245–274. Bibcode:1975InMat

Professor at the University of Copenhagen. His research interests include homotopy theory, algebraic K-theory, and arithmetic algebraic geometry. Hesselholt

construction the converse is also true. This can be formulated in terms of homotopy theory. Recall B G {\displaystyle BG} the classifying space for stable spherical

no. 3, 623–637. 2001 Michael J. Hopkins for: Nilpotence and stable homotopy theory. I. Ann. of Math. (2) 128 (1988), no. 2, 207–241. (with Ethan Devinatz

regarding general localization theory, as they occur in the context of homotopy theory. He has also conducted research in the field of cohomology of groups

rings, intersection theory, (equivariant) algebraic K-theory, motivic homotopy theory, and existence of vector bundles on singular algebraic surfaces. Around

Technology, under the supervision of Michael Artin, (Fibrations in Étale Homotopy Theory). He was a postdoctoral instructor at Princeton University: a lecturer

generalization of the connectivity part of the theorem from traditional homotopy theory to any other infinity-topos with an infinity-site of definition was

Hopkins, Michael J.; Smith, Jeffrey H. (1988). "Nilpotence and stable homotopy theory. I". Annals of Mathematics. 128 (2): 207–241. doi:10.2307/1971440.

{\displaystyle {\binom {t+k}{k}}} . Johnson, Keith (2014), "Stable homotopy theory, formal group laws, and integer-valued polynomials", in Fontana, Marco;

G have been obtained by Asok, Hoyois & Wendt (2018) by means of A1 homotopy theory. Bass, H. (1973), Some problems in 'classical' algebraic K-theory.

In mathematics, topological groups are the combination of groups and topological spaces, i.e. they are groups and topological spaces at the same time,

James E. Humphreys (1997, ISBN 978-0-387-90053-7) A Course in Simple-Homotopy Theory, Marshall. M. Cohen, (1973, ISBN 0-387-90056-X) Functions of One Complex

group of integers. The homotopy hypothesis, a well-known conjecture in homotopy theory formulated by Alexander Grothendieck, states that a suitable generalization

Riehl (2021), for "deep and foundational work in category theory and homotopy theory". Kristen Hendricks (2023), for "highly influential work on equivariant

and pointwise multiplication are homotopic. Thus, in terms of the homotopy theory of ΩG, these maps are interchangeable. Loop groups were used to explain

an arbitrary integer. This was a major addendum to the existing n-Homotopy theory. After graduating from Tbilisi State University, he became a research

motivic homotopy theory as well as finding a way to build algebraic varieties with a specified list of properties. From the motivic homotopy theory the proof

the Steinberg relation. In motivic cohomology, specifically motivic homotopy theory, there is a sheaf K n , A {\displaystyle K_{n,A}} representing a generalization

arXiv:math/0608040. ISBN 978-0-691-14048-3. Simpson, Carlos (2012). Homotopy theory of higher categories. New Mathematical Monographs. Vol. 19. Cambridge:

Fellowship and in 1972 the Leroy P. Steele Prize for his paper Simplicial homotopy theory. Curtis died in Seattle, Washington on April 2, 2024, at the age of

Poincaré duality Poitou–Tate duality Pontryagin duality S-duality (homotopy theory) Schur–Weyl duality Series-parallel duality Serre duality Spanier–Whitehead

Springer Robinson, Alan (1983), "Derived tensor products in stable homotopy theory", Topology, 22 (1): 1–18, doi:10.1016/0040-9383(83)90042-3, MR 0682056

1/30144. Mathew, Akhil; Meier, Lennart (2013). "Affineness and chromatic homotopy theory". Journal of Topology. 8 (2): 476–528. arXiv:1311.0514. doi:10.1112/jtopol/jtv005

algebraic topology model of a differential graded algebra used in rational homotopy theory. Neron minimal model, algebraic geometry model for abelian varieties

New York: Springer. ISBN 9780387215976. OCLC 55897585. Cohen, Marshall M. (1973) A Course in Simple-Homotopy Theory, Springer-Verlag New York v t e

Ravenel, Douglas C. (1992), Nilpotence and Periodicity in Stable Homotopy Theory, Annals of mathematics studies, vol. 128, Princeton University Press

ISBN 0-521-81496-0 (Page 29) Goerss, P. G.; Jardine, J. F. (1999), Simplicial Homotopy Theory, Progress in Mathematics, vol. 174, Basel, Boston, Berlin: Birkhäuser

Hilton, Peter (1988), "A Brief, Subjective History of Homology and Homotopy Theory in This Century", Mathematics Magazine, 60 (5), Mathematical Association

Differential graded Lie algebra Quillen, Daniel (September 1969). "Rational homotopy theory". Annals of Mathematics. 2. 90 (2): 205–295. doi:10.2307/1970725. JSTOR 1970725

(as of 2013) (Accessed 1 April 2020) Kerodon a Stacks project inspired online textbook on categorical homotopy theory maintained by Jacob Lurie v t e

2012: Michael J. Hopkins "For his leading role in the development of homotopy theory, which has both reinvigorated algebraic topology as a central field

nerve of a category. Goerss, Paul; Jardine, John (2009), Simplicial Homotopy Theory, Progress in Mathematics, vol. 174, Birkhäuser Basel, ISBN 978-3-7643-6064-1

one publication so far, published when he was doing his PhD. "On ex-homotopy theory and generalized homotopy products". The University of Hong Kong. 1978

homotopy equivalent but not homeomorphic. This was the origin of simple homotopy theory. The use of the term geometric topology to describe these seems to

Algebraic K {\displaystyle K} -theory of spaces, concordance, and stable homotopy theory, Algebraic topology and algebraic K {\displaystyle K} -theory (Princeton

1155/S1073792804132017, ISSN 1073-7928, MR 2037049 Quillen, Daniel (1969), "Rational homotopy theory", Annals of Mathematics, Second Series, 90 (2): 205–295, doi:10.2307/1970725

Strecker, theorem 12.7, page 213 Riehl, Emily (2014). Categorical Homotopy Theory. New York: Cambridge University Press. p. 32. ISBN 9781139960083. OCLC 881162803

Grothendieck. He also collaborated with Barry Mazur to define étale homotopy theory which has become an important tool in algebraic geometry, and applied

higher-dimensional groupoids, not available in group theory, with applications in homotopy theory and in group cohomology. Brown, R.; Higgins, P.J. (1981). "On the algebra

MR 1268594 Röndigs, Oliver; Østvær, Paul Arne (2008), "Rigidity in motivic homotopy theory", Mathematische Annalen, 341 (3): 651–675, doi:10.1007/s00208-008-0208-5

Grothendieck-Teichmüller Groups: Part 2: The Applications of (Rational) Homotopy Theory Methods, Mathematical Surveys and Monographs, vol. 217, American Mathematical

meanings: Spectrum (topology), the fundamental object of study in stable homotopy theory Spectrum of a C*-algebra, a kind of dual object Spectrum of a ring

invariant problem", in Mahowald, Mark E.; Priddy, Stewart (eds.), Homotopy theory via algebraic geometry and group representations (Evanston, IL, 1997)

S2CID 242258794 Puppe, Dieter (1962), "On the formal structure of stable homotopy theory", Colloquium on algebraic topology, Aarhus Universitet Matematisk Institute

information and provide a diagram calculus to use in derived categories and homotopy theory. Formally, a prederivator D {\displaystyle \mathbb {D} } is a 2-functor

Jean-Pierre Marquis (2006) "A path to Epistemology of Mathematics: Homotopy theory", pages 239 to 260 in The Architecture of Modern Mathematics, J. Ferreiros

Mathematics Institutions Johns Hopkins University Thesis On stable homotopy theory and some applications (1965) Doctoral advisor C. T. C. Wall Website

Proposition 5.7. Frankland, Martin (February 4, 2013). "Math 527 - Homotopy Theory – Compactly generated spaces" (PDF). Steenrod, N. E. (1 May 1967).

computation of stable stems in The Čech centennial: a Conference on Homotopy Theory, June 22–26, 1993, pp. 299–316. MR1320997 Mark E. Mahowald, A new infinite

Proposition 5.7. Frankland, Martin (February 4, 2013). "Math 527 - Homotopy Theory – Compactly generated spaces" (PDF). Steenrod, N. E. (1 May 1967).

mathematical physics. In the 1960s he wrote fundamental papers on higher homotopy theory and homotopy algebras. He introduced A ∞ {\displaystyle A_{\infty }}

E_n-ring What is a simplicial commutative ring from the point of view of homotopy theory? What facts in commutative algebra fail miserably for simplicial commutative

the path space fibration. mapping space Martin Frankland, Math 527 - Homotopy Theory - Fiber sequences Davis & Kirk 2001, Definition 6.14. Davis & Kirk

if and only if it is fibrant in the sense of so-called "holomorphic homotopy theory". Every compact smooth manifold of dimension 2n, which has only handles

1016/0040-9383(73)90014-1. MR 0391071. Brown, Edgar H. (1965). "Abstract homotopy theory". Transactions of the American Mathematical Society. 119 (1): 79–85

Corporation, p. 37, ISBN 9780486783475. Riehl, Emily (2014), Categorical Homotopy Theory, New Mathematical Monographs, vol. 24, Cambridge University Press,

Robert; Lambrechts, Pascal; Turchin, Victor; Volić, Ismar (2011). "Real homotopy theory of semi-algebraic sets". Algebraic & Geometric Topology. 11 (5): 2477–2545

conjecture Mathew, Akhil; Meier, Lennart (2015). "Affineness and chromatic homotopy theory". Journal of Topology. 8 (2): 476–528. arXiv:1311.0514. doi:10.1112/jtopol/jtv005

crystals and for excitations in superfluid 3He, is the topological homotopy theory. Density functional theory, classical molecular dynamics and kinetic

Cenkl M., Miller, H. (ed.) The Cech centennial: Proc. Conference on Homotopy Theory, Contemporary Mathematics, 181, 1995, pp. 405–418 With Elliot Gootman:

object at the nLab Goerss, Paul G.; Jardine, John F. (1999). Simplicial Homotopy Theory. Progress in Mathematics. Vol. 174. Basel, Boston, Berlin: Birkhäuser

{\displaystyle T\leftarrow P\to X\to X/G} . Jardine, John F. (2015). Local homotopy theory. Springer Monographs in Mathematics. New York: Springer-Verlag. section

the nLab category of presheaves at the nLab Free cocompletion at the nLab Daniel Dugger, Sheaves and Homotopy Theory, the pdf file provided by nlab.

May (b. 1939), researcher in algebraic topology, category theory, homotopy theory, and the foundational aspects of spectra Barry Mazur (b. 1937) Curtis

1090/pspum/062.2/1492538, MR 1492538, S2CID 2659059 Simpson, Carlos (2012). Homotopy theory of higher categories. New Mathematical Monographs. Vol. 19. Cambridge:

functor Change of rings May, J.P.; Sigurdsson, J. (2006). Parametrized Homotopy Theory. A.M.S. p. 253. ISBN 0-8218-3922-5. Bourbaki, Nicolas (1989), Elements

Ravenel, Douglas C. (1980), "Complex cobordism and its applications to homotopy theory", Proceedings of the International Congress of Mathematicians (Helsinki

Østvær, P.A.; Röndigs, Oliver; Voevodsky, Vladimir (2007), Motivic Homotopy Theory: Lectures at a Summer School in Nordfjordeid, Norway, August 2002,

1136/bjophthalmol-2014-304986. PMID 24568871. Gromov, Mikhael (1999). "Quantitative Homotopy Theory". In Rossi, Hugo (ed.). Prospects in Mathematics: Invited Talks on

Pierre; Griffiths, Phillip; Morgan, John; Sullivan, Dennis (1975), "Real homotopy theory of Kähler manifolds", Inventiones Mathematicae, 29 (3): 245–274, Bibcode:1975InMat

open map. Baues, Hans-Joachim; Quintero, Antonio (2001). Infinite Homotopy Theory. K-Monographs in Mathematics. Vol. 6. p. 53. ISBN 9780792369820. A

(1986), "Through the looking glass: a dictionary between rational homotopy theory and local algebra", in J.-E. Roos (ed.), Algebra, algebraic topology

ISSN 0003-486X, JSTOR 1970299 Marshall M. Cohen (1973), "A Course in Simple-Homotopy Theory", Graduate Texts in Mathematics, Graduate Texts in Mathematics, vol

X)=X^{H}} . Greenlees, John; May, Peter (1995). "8. Equivariant stable homotopy theory" (PDF). In James, I.M. (ed.). Handbook of algebraic topology. Elsevier

Hermann. ISBN 2-7056-6049-6. six operations at the nLab What (if anything) unifies stable homotopy theory and Grothendieck's six functors formalism?

Cambridge. Kim has made contributions to the application of arithmetic homotopy theory to the study of Diophantine problems, especially to finiteness theorems

MR 1989190. Hopkins, M and Mahowald, M., From Elliptic Curves to Homotopy Theory (1998), http://www.math.purdue.edu/research/atopology/Hopkins-Mahowald/eo2homotopy

of Deligne's Hochschild cohomology conjecture". Recent progress in homotopy theory (Baltimore, MD, 2000). Providence, RI: Amer. Math. Soc. pp. 153–193

Texts in Mathematics 139, 1993. Cohen, Marshall M., A Course in Simple-Homotopy Theory, Springer Graduate Texts in Mathematics 10, 1973. Brody, E. J. (1960)

abroad, Warner was now on the margins of her Oxford-era interest of homotopy theory research, much of her knowledge obsolete due to significant advancements

module. This leads to the idea of using multiple groupoid objects in homotopy theory. More generally, the Eckmann–Hilton argument is a special case of the

homeomorphism) by invariants has motivated areas of research, such as homotopy theory, homology theory, and K-theory. A given set may have many different

MR 0212840 Hatcher, A.E. (1978). "Concordance spaces, higher simple-homotopy theory, and applications". Algebraic and geometric topology (Proc. Sympos

way responsible for much of the subtlety and complication in stable homotopy theory. An important generalisation to the non-abelian case using crossed

55P15, 55Q05 18C10, 18D05, 18G55, 55P15, 55Q05]. Dimitri Ara. On the homotopy theory of Grothendieck ∞ -groupoids. J. Pure Appl. Algebra, 217(7):1237–1278

Hu, Sze-Tsen (1971) [1959]. "Chapter VII. Cohomotopy Groups" (PDF). Homotopy theory (PDF). Academic Press. pp. 205–228. LCCN 59-11526. Retrieved August

(2005), "La théorie de l'homotopie de Grothendieck" [Grothendieck's homotopy theory] (PDF), Astérisque, 301, MR 2200690 Denis-Charles Cisinski (2006),

Theory, Terence Tao (2011, ISBN 978-0-8218-6919-2) 127 Modern Classical Homotopy Theory, Jeffrey Strom (2011, ISBN 978-0-8218-5286-6) 128 Tensors: Geometry

Cisinski, Denis-Charles; Khan, Adeel A. (2017-05-09). "Brave new motivic homotopy theory II: Homotopy invariant K-theory". arXiv:1705.03340 [math.AT]. Behrend

Chow groups. One of the motivations for higher Chow groups comes from homotopy theory. In particular, if α , β ∈ Z ∗ ( X ) {\displaystyle \alpha ,\beta \in

bundle, known as the tangent bundle along the fibers of f. Using A1-homotopy theory, the Grothendieck–Riemann–Roch theorem has been extended by Navarro

Félix, Yves; Halperin, Stephen; Thomas, Jean-Claude (2001). Rational homotopy theory. Graduate Texts in Mathematics. Vol. 205. New York: Springer-Verlag

Pontryagin, L. S. (1959). "Smooth manifolds and their applications in homotopy theory" (PDF). American Mathematical Society Translations. Series 2. 11. Translated

Inventiones Mathematicae 3 (1967), 172–178, EuDML. The case of simplicial sets is treated in Paul Goerss, Rick Jardine, Simplicial homotopy theory, Birkhäuser

Microsoft Research 1951 2008 Rick Jardine University of Western Ontario Homotopy theory 2008 Angus Macintyre University of Oxford Logic 1941 2008 Cameron Leigh

1007/BF02684690, MR 0174605, S2CID 4649786 Cohen, M. A course in simple homotopy theory Graduate Text in Mathematics 10, Springer, 1973 Higman, Graham (1940)

Monographs, American Mathematical Society, (2007), Emily Riehl, Categorical Homotopy Theory, Cambridge University Press (2014) [1] Cisinski, Denis-Charles (2023)

Mathematical Society, 1972. 1972 Edward B. Curtis for his paper, Simplicial homotopy theory, Advances in Mathematics, volume 6 (1971), pp. 107–209. 1972 William

homotopī-ron)" [S1-action on the cohomologic complex projection space (same homotopy theory)] (PDF). RIMS Kokyuroku (in Japanese). 319. Kyoto University: 20–25

foundations of the usual theories of logic and connect logic with homotopy theory by introducing a Hopf structure into the generalized logic theories

homotopī-ron)" [S1-action on the cohomologic complex projection space (same homotopy theory)] (PDF). RIMS Kokyuroku (in Japanese). 319. Kyoto University: 20–25

families, and it is not amenable to computation. Vladimir Voevodsky, A1-homotopy theory, Proceedings of the International Congress of Mathematicians, Vol.

Surv. Math. Sci. 1 (2014), 153–240. Jardine, John F. (2015). Local homotopy theory. Springer Monographs in Mathematics. New York: Springer-Verlag. doi:10

homology either. The homology "stabilizes" in the sense of stable homotopy theory: there is an inclusion map Sn → Sn+1, and for fixed k, the induced

wide-ranging techniques drawn from analytic number theory, ergodic theory, homotopy theory to address concrete problems in number theory and discover new phenomena

"Introduction to the Language of Stacks and Gerbes". Retrieved 2007-05-20. Homotopy theory of presheaves of simplicial groupoids, Zhi-Ming Luo Twisted K-theory

Hilton, Peter (1988), "A Brief, Subjective History of Homology and Homotopy Theory in This Century", Mathematics Magazine, 60 (5), Mathematical Association

conjecture⇐de Branges's theorem 1984 Gunnar Carlsson Segal's conjecture homotopy theory 1984 Haynes Miller Sullivan conjecture classifying spaces Miller proved

sampling of 2-categorical aspects of quasi-category theory", Categorical Homotopy Theory, Cambridge: Cambridge University Press, pp. 318–336, doi:10.1017/cbo9781107261457

Daniel S.; Hopkins, Michael J. (2013). "Chern-Weil forms and abstract homotopy theory". Bulletin of the American Mathematical Society. (N.S.). 50 (3): 431–468

_{2}(B(S^{-1}S)^{0})\to \pi _{1}(Ff)\to \pi _{1}(BGL(R))=GL(R)\to K_{1}(R).} From homotopy theory, we know the second term is central; i.e., π 1 ( F f ) → E ( R ) {\displaystyle

MR 2900173. Rourke, Colin P.; Sanderson, Brian J. (1971). "Δ-Sets I: Homotopy Theory". Quarterly Journal of Mathematics. 22 (3): 321–338. Bibcode:1971QJMat

ISSN 0273-0979. Belmont, Eva (2016-05-16). "Talbot 2016: Equivariant homotopy theory and the Kervaire invariant one problem" (PDF). math.northwestern.edu

S2CID 15403121 Lev Pontryagin, Smooth manifolds and their applications in homotopy theory American Mathematical Society Translations, Ser. 2, Vol. 11, pp. 1–114

construct an analogue of the functor R f ! {\displaystyle Rf_{!}} in A1-homotopy theory. Grothendieck's relative point of view in algebraic geometry Change

Brown, R.; Sivera, R. (2009). "Algebraic colimit calculations in homotopy theory using fibred and cofibred categories". Theory and Applications of Categories

Hilton, Peter (1988), "A Brief, Subjective History of Homology and Homotopy Theory in this Century", Mathematics Magazine, 60 (5): 282–291, doi:10.1080/0025570X

no. 1. p. 1-2. Lyra, Carlos Benjamin de (1965). "On a conjecture in homotopy theory". Anais da Academia Brasileira de Ciências. Vol. 37, no. 2. p. 167-184

first 9 pages of [1] mention some examples of incorrect results in homotopy theory. Ilya Nikokoshev, Most interesting mathematics mistake? Kevin Buzzard

Martin C. (2008) [1968], Cohomology operations and applications in homotopy theory, Mineola, NY: Dover Publications, ISBN 978-0-486-46664-4, MR 0226634

physicist Emil Hilb (1882–1929), mathematician Peter Hilton (1923–2010), homotopy theory Edith Hirsch Luchins (1921–2002), mathematician Kurt Hirsch (1906–1986)

requires |journal= (help) Jardine, J. F. (2020-10-26). "Persistent homotopy theory". arXiv:2002.10013 [math.AT]. Lesnick, Michael; Wright, Matthew (2022)

anti-feminist activist Julie Bergner, American expert on algebraic topology, homotopy theory, and higher category theory Nicole Berline (born 1944), French researcher

relating the groups Ω i a l m {\displaystyle \Omega _{i}^{alm}} to stable homotopy theory. The generalized Poincaré conjecture in dimension n {\displaystyle

if and only if it is fibrant in the sense of so-called "holomorphic homotopy theory". Meromorphic function in one-variable complex function were studied

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Whitehead, Newmanry mathematician (topologist, one of the founders of homotopy theory) Bernard Willson, academic, worked in Hut 4 on Italian and Japanese

those whose negative homotopy groups vanish. (In areas related to homotopy theory, it is common to use homological conventions, as opposed to cohomological

Study, US "He defined and developed motivic cohomology and the A1-homotopy theory, provided a framework for describing many new cohomology theories for