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searching for Riemann sphere 29 found (203 total)

Quasi-Fuchsian group (331 words) [view diff] exact match in snippet view article find links to article

quasi-Fuchsian groups of type 1), as their limit sets are proper subsets of the Riemann sphere. The special case when the Jordan curve is a circle or line is called

Knizhnik–Zamolodchikov equations (3,059 words) [view diff] exact match in snippet view article find links to article

differential equations satisfied by the correlation functions (on the Riemann sphere) of two-dimensional conformal field theories associated with an affine

Lattès map (106 words) [view diff] exact match in snippet view article find links to article

l'Académie des sciences, 166: 26–28 Milnor, John Willard (2006), "On Lattès maps", Dynamics on the Riemann sphere, Eur. Math. Soc., pp. 9–43, MR 2348953

Character variety (1,237 words) [view diff] exact match in snippet view article find links to article

{\displaystyle G=\mathrm {SL} (2,\mathbb {C} )} and X {\displaystyle X} is the Riemann sphere punctured three times, so π = π 1 ( X ) {\displaystyle \pi =\pi _{1}(X)}

Fuchsian model (662 words) [view diff] exact match in snippet view article find links to article

Riemann surface R {\displaystyle R} which is not isomorphic to either the Riemann sphere (the elliptic case) or a quotient of the complex plane by a discrete

Field of definition (1,617 words) [view diff] exact match in snippet view article find links to article

definition.) Viewing the real projective line as being the equator on the Riemann sphere, the coordinate-wise action of complex conjugation on the complex projective

Non-positive curvature (660 words) [view diff] exact match in snippet view article find links to article

infinite family of homeomorphism types of such surfaces whereas the Riemann sphere is the only closed, orientable Riemann surface of constant Gaussian

Bodil Branner (489 words) [view diff] exact match in snippet view article find links to article

2015-02-16. Hjorth, Poul G.; Petersen, Carsten Lunde (2006), Dynamics on the Riemann sphere: A Bodil Branner Festschrift, Including papers from the Symposium on

Andrei Bolibrukh (425 words) [view diff] exact match in snippet view article find links to article

Riemann-Hilbert problem and Fuchsian differential equations on the Riemann sphere". In: Proceedings of the International Congress of Mathematicians. Birkhäuser

Ahlfors theory (1,195 words) [view diff] exact match in snippet view article find links to article

the Five Island theorem. Let D1,...,D5 be five Jordan regions on the Riemann sphere with disjoint closures. Then there exists a constant c, depending only

Branched covering (1,702 words) [view diff] case mismatch in snippet view article find links to article

Geometry, Berlin, New York: Springer-Verlag, ISBN 978-0-387-90244-9, MR 0463157, OCLC 13348052 Osserman, Brian, Branched Covers of the Riemann Sphere (PDF)

Octahedral symmetry (1,867 words) [view diff] exact match in snippet view article find links to article

called the Bolza curve, is obtained as the ramified double cover of the Riemann sphere, with ramification locus at the set of vertices of the regular inscribed

Leila Schneps (2,410 words) [view diff] case mismatch in snippet view article find links to article

ISBN 9780521478212 Schneps, Leila (1994), "Dessins d'enfants on the Riemann Sphere" (PDF), The Grothendieck Theory of Dessins d'Enfants, 200: 47–78, doi:10

Spherical braid group (424 words) [view diff] exact match in snippet view article find links to article

Nick (2020). "Section problems for configurations of points on the Riemann sphere". Algebraic and Geometric Topology. 20 (6): 3047–3082. arXiv:1807.10171

Wess–Zumino–Witten model (3,665 words) [view diff] exact match in snippet view article find links to article

identities. If the Riemann surface Σ {\displaystyle \Sigma } is the Riemann sphere, correlation functions of affine primary fields obey Knizhnik–Zamolodchikov

Moduli space (4,048 words) [view diff] exact match in snippet view article find links to article

their number. There is exactly one complex curve of genus zero, the Riemann sphere, and its group of isomorphisms is PGL(2). Hence, the dimension of M

Twistor theory (4,205 words) [view diff] case mismatch in snippet view article find links to article

Piotr (2015-09-16). "Loop Integrands for Scattering Amplitudes from the Riemann Sphere". Physical Review Letters. 115 (12): 121603. arXiv:1507.00321. Bibcode:2015PhRvL

Constant-mean-curvature surface (2,044 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \phi :V\rightarrow \mathbb {C} } is a harmonic function into the Riemann sphere. If ϕ z ¯ ≠ 0 {\displaystyle \phi _{\bar {z}}\neq 0} then X : V → R

Hyperbolic spiral (2,592 words) [view diff] exact match in snippet view article find links to article

David; Series, Caroline; Wright, David (2002), "Inversions and the Riemann sphere", Indra's Pearls: The Vision of Felix Klein, Cambridge University Press

Chern–Weil homomorphism (2,779 words) [view diff] exact match in snippet view article find links to article

projective line; see Chern class#Example: the complex tangent bundle of the Riemann sphere. Since Ω E ⊗ E ′ = Ω E ⊗ I E ′ + I E ⊗ Ω E ′ {\displaystyle \Omega _{E\otimes

Poincaré half-plane model (3,972 words) [view diff] exact match in snippet view article find links to article

two given circles. The projective linear group PGL(2,C) acts on the Riemann sphere by the Möbius transformations. The subgroup that maps the upper half-plane

Two-dimensional conformal field theory (5,446 words) [view diff] exact match in snippet view article find links to article

whose correlation functions are therefore not single-valued on the Riemann sphere. Three-point structure constants also appear in OPEs, V 1 ( z 1 ) V

Congruence subgroup (4,782 words) [view diff] exact match in snippet view article find links to article

\Gamma _{0}(p)^{+}} ⁠) has genus zero (i.e., the modular curve is a Riemann sphere) if and only if ⁠ p {\displaystyle p} ⁠ is 2, 3, 5, 7, 11, 13, 17, 19

Icosahedral symmetry (2,333 words) [view diff] exact match in snippet view article find links to article

of a Belyi surface – a Riemann surface with a holomorphic map to the Riemann sphere, ramified only at 0, 1, and infinity (a Belyi function) – the cusps

Function of several complex variables (17,684 words) [view diff] exact match in snippet view article find links to article

meromorphic functions. A compact one-dimensional complex manifold was a Riemann sphere C ^ ≅ C P 1 {\displaystyle {\widehat {\mathbb {C} }}\cong \mathbb {CP}

Topological recursion (4,387 words) [view diff] exact match in snippet view article find links to article

\mu =(\mu _{1},\dots ,\mu _{n})} : the number of branch covers of the Riemann sphere by a genus g connected surface, with 2g-2+n simple ramification points

Tau function (integrable systems) (6,689 words) [view diff] exact match in snippet view article

_{1}({\bf {P}}^{1}\backslash \{\alpha _{i}\}_{i=1,\dots ,n})} of the Riemann sphere punctured at the points { α i } i = 1 , … , n {\displaystyle \{\alpha

W-algebra (5,418 words) [view diff] exact match in snippet view article find links to article

{\displaystyle L_{-1}V(z)={\frac {\partial }{\partial z}}V(z)} . On the Riemann sphere, if there is no field at infinity, we have W ( h ) ( y ) = y → ∞ O (

Beltrami equation (10,901 words) [view diff] exact match in snippet view article find links to article

|^{2})|e^{2k}|}} is nowhere vanishing. Since f induces a smooth map of the Riemann sphere C ∪ ∞ into itself which is locally a diffeomorphism, f must be a diffeomorphism