Differential topology: Differential geometry, Sphere, Vector field, Tangent space, Symplectic manifold, Cotangent space, Embedding, Atlas, Chain ... Orbifold, Differentiable manifold, Jet bundle - Softcover

Differential topology

Taschenbuch. Zustand: Neu. Neuware -Source: Wikipedia. Pages: 147. Chapters: Differential geometry, Sphere, Vector field, Tangent space, Symplectic manifold, Cotangent space, Embedding, Atlas, Chain complex, Partition of unity, Stokes' theorem, Orbifold, Differentiable manifold, Jet bundle, Introduction to gauge theory, Cobordism, Lie derivative, Vector bundle, Fiber bundle, Frobenius theorem, Exotic sphere, Immersion, Connection, Classification of manifolds, Orientability, Eisenbud¿Levine¿Khimshiashvili signature formula, Contact geometry, Tensor field, Tangent bundle, Implicit and explicit functions, Nonholonomic system, Whitney embedding theorem, Connected sum, Line bundle, Associated bundle, Inverse function theorem, Massey product, Transversality, Kervaire invariant, Cerf theory, Fibration, Hairy ball theorem, Reduction of the structure group, Yamabe invariant, Lie bracket of vector fields, Cotangent bundle, Pontryagin class, Current, Serre¿Swan theorem, Integrability conditions for differential systems, Clutching construction, Submanifold, Transversality theorem, H-cobordism, Whitney topologies, Atiyah¿Bott fixed-point theorem, Whitney conditions, Pseudogroup, Normal bundle, Unit tangent bundle, Smale's paradox, Canonical coordinates, Section, Glossary of differential geometry and topology, Mazur manifold, Congruence, Poincaré¿Hopf theorem, L cohomology, Vector flow, Conley index theory, Minimax eversion, Vector fields on spheres, Lie algebra bundle, Obstruction theory, Spinor bundle, Vertical bundle, Regular homotopy, Parallelizable manifold, Covariant classical field theory, Seifert conjecture, Pseudoisotopy theorem, Whitney umbrella, Riemann¿Roch theorem for smooth manifolds, Whitney immersion theorem, Horizontal bundle, Donaldson's theorem, Double, Stunted projective space, Symplectization, Donaldson theory, Critical value, Atiyah conjecture, Band sum, Kervaire manifold, Sharp map, Disc theorem, Inverse bundle, Ehresmann's theorem, Horizontal form, Flat map, Polyvector field, Top-dimensional form, Symplectic space. Excerpt: This terminology should not be blamed on me. It was obtained by a democratic process in my course of 1976-77. An orbifold is something with many folds; unfortunately, the word ¿manifold¿ already has a different definition. I tried ¿foldamani¿, which was quickly displaced by the suggestion of ¿manifolded¿. After two months of patiently saying ¿no, not a manifold, a manifol,¿ we held a vote, and ¿orbifold¿ won. In the mathematical disciplines of topology, geometry, and geometric group theory, an orbifold (for 'orbit-manifold') is a generalization of a manifold. It is a topological space (called the underlying space) with an orbifold structure (see below). The underlying space locally looks like the quotient space of a Euclidean space under the linear action of a finite group. Definitions of orbifold have been given several times: by Satake in the context of automorphic forms in the 1950s under the name V-manifold; by Thurston in the context of the geometry of 3-manifolds in the 1970s when he coined the name orbifold, after a vote by his students; and by Haefliger in the 1980s in the context of Gromov's programme on CAT(k) spaces under the name orbihedron. The definition of Thurston will be described here: it is the most widely used and is applicable in all cases. Mathematically, orbifolds arose first as surfaces with singular points long before they were formally defined. One of the first classical examples arose in the theory of modular forms.Books on Demand GmbH, Überseering 33, 22297 Hamburg 148 pp. Englisch. Artikel-Nr. 9781157594420

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