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searching for singular homology 17 found (94 total)

William S. Massey (461 words) [view diff] exact match in snippet view article find links to article

Dekker. 1978; xiv+412 pp.{{cite book}}: CS1 maint: postscript (link) Singular homology theory. Graduate Texts in Mathematics. Springer-Verlag. 1980; xii+265

De Rham theorem (1,493 words) [view diff] exact match in snippet view article find links to article

However, a technical result implies that the singular homology groups coincide with smooth singular homology groups. This shows that the de Rham theorem

Homology manifold (253 words) [view diff] exact match in snippet view article find links to article

they are isomorphic to G. Here H is some homology theory, usually singular homology. Homology manifolds are the same as homology Z-manifolds. More generally

Lefschetz hyperplane theorem (1,762 words) [view diff] exact match in snippet view article find links to article

{\displaystyle H_{k}(Y,\mathbb {Z} )\rightarrow H_{k}(X,\mathbb {Z} )} in singular homology is an isomorphism for k < n − 1 {\displaystyle k<n-1} and is surjective

Bredon cohomology (96 words) [view diff] exact match in snippet view article find links to article

ISBN 978-3-540-34973-0, MR 0214062 Illman, Sören (1973), "Equivariant singular homology and cohomology", Bulletin of the American Mathematical Society, 79:

Cofibration (1,643 words) [view diff] exact match in snippet view article find links to article

technical notion of good pair which has the same long exact sequence in singular homology associated to a cofibration, but it is not equivalent. The notion

Homotopy (3,271 words) [view diff] no match in snippet view article find links to article

and only if Y is. X is simply connected if and only if Y is. The (singular) homology and cohomology groups of X and Y are isomorphic. If X and Y are path-connected

Reduced homology (537 words) [view diff] exact match in snippet view article find links to article

Cambridge University Press, ISBN 0-521-79540-0. Detailed discussion of homology theories for simplicial complexes and manifolds, singular homology, etc.

Alexandrov topology (2,160 words) [view diff] exact match in snippet view article find links to article

American Mathematical Society, 2009, p.170ff McCord, M. C. (1966). "Singular homology and homotopy groups of finite topological spaces". Duke Mathematical

Graduate Texts in Mathematics (4,909 words) [view diff] case mismatch in snippet view article find links to article

Cyclotomic Fields II, Serge Lang (1980, ISBN 978-1-4684-0088-5) Singular Homology Theory, William S. Massey (1980, ISBN 978-1-4684-9233-0) Riemann Surfaces

Morse theory (3,396 words) [view diff] exact match in snippet view article find links to article

is, independent of the function and metric) and isomorphic to the singular homology of the manifold; this implies that the Morse and singular Betti numbers

H topology (1,891 words) [view diff] exact match in snippet view article find links to article

1007/BF01587941, MR 1403354 Suslin, Andrei; Voevodsky, Vladimir (1996), "Singular homology of abstract algebraic varieties", Inventiones Mathematicae, 123 (1):

Finite topological space (2,613 words) [view diff] exact match in snippet view article find links to article

1090/s0002-9947-1966-0195042-2. MR 0195042. McCord, Michael C. (1966). "Singular homology groups and homotopy groups of finite topological spaces" (PDF). Duke

Leroy P. Steele Prize (2,236 words) [view diff] exact match in snippet view article find links to article

to topology and algebra, in particular for his classic papers on singular homology and his work on axiomatic homology theory which had a profound influence

Eilenberg–MacLane space (3,349 words) [view diff] exact match in snippet view article find links to article

{\displaystyle q\neq 0} , h ∗ {\displaystyle h_{*}} agrees with reduced singular homology H ~ ∗ ( ⋅ , G ) {\displaystyle {\tilde {H}}_{*}(\cdot ,G)} with coefficients

Gerbe (3,462 words) [view diff] exact match in snippet view article find links to article

B^{2}(U(1))]=[X,K(\mathbb {Z} ,3)]} , which is exactly the third singular homology group H 3 ( X , Z ) {\displaystyle H^{3}(X,\mathbb {Z} )} . It has

Sheaf cohomology (5,832 words) [view diff] exact match in snippet view article find links to article

13.) Barratt, M. G.; Milnor, John (1962), "An example of anomalous singular homology", Proceedings of the American Mathematical Society, 13 (2): 293–297