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- Homotopy_sphere abstract "In algebraic topology, a branch of mathematics, a homotopy sphere is an n-manifold that is homotopy equivalent to the n-sphere. It thus has the same homotopy groups and the same homology groups as the n-sphere, and so every homotopy sphere is necessarily a homology sphere.The topological generalized Poincaré conjecture is that any n-dimensional homotopy sphere is homeomorphic to the n-sphere; it was solved by Stephen Smale in dimensions five and higher, by Michael Freedman in dimension 4, and for dimension 3 by Grigori Perelman in 2005.The resolution of the smooth Poincaré conjecture in dimensions 5 and larger implies that homotopy spheres in those dimensions are precisely exotic spheres. It is still an open question (as of 2014) whether or not there are non-trivial smooth homotopy spheres in dimension 4.".
- Homotopy_sphere wikiPageID "1202074".
- Homotopy_sphere wikiPageLength "1259".
- Homotopy_sphere wikiPageOutDegree "19".
- Homotopy_sphere wikiPageRevisionID "620683367".
- Homotopy_sphere wikiPageWikiLink Algebraic_topology.
- Homotopy_sphere wikiPageWikiLink Category:Homotopy_theory.
- Homotopy_sphere wikiPageWikiLink Category:Topological_spaces.
- Homotopy_sphere wikiPageWikiLink Exotic_sphere.
- Homotopy_sphere wikiPageWikiLink Generalized_Poincaré_conjecture.
- Homotopy_sphere wikiPageWikiLink Grigori_Perelman.
- Homotopy_sphere wikiPageWikiLink Homeomorphic.
- Homotopy_sphere wikiPageWikiLink Homeomorphism.
- Homotopy_sphere wikiPageWikiLink Homology_(mathematics).
- Homotopy_sphere wikiPageWikiLink Homology_sphere.
- Homotopy_sphere wikiPageWikiLink Homotopy.
- Homotopy_sphere wikiPageWikiLink Homotopy_group.
- Homotopy_sphere wikiPageWikiLink Homotopy_groups_of_spheres.
- Homotopy_sphere wikiPageWikiLink Manifold.
- Homotopy_sphere wikiPageWikiLink Mathematics.
- Homotopy_sphere wikiPageWikiLink Michael_Freedman.
- Homotopy_sphere wikiPageWikiLink Poincaré_conjecture.
- Homotopy_sphere wikiPageWikiLink Sphere.
- Homotopy_sphere wikiPageWikiLink Stephen_Smale.
- Homotopy_sphere wikiPageWikiLinkText "Homotopy sphere".
- Homotopy_sphere wikiPageWikiLinkText "homotopy ''n''-sphere".
- Homotopy_sphere wikiPageWikiLinkText "homotopy ''n''-spheres".
- Homotopy_sphere wikiPageWikiLinkText "homotopy 4-sphere".
- Homotopy_sphere wikiPageWikiLinkText "homotopy sphere".
- Homotopy_sphere hasPhotoCollection Homotopy_sphere.
- Homotopy_sphere wikiPageUsesTemplate Template:Topology-stub.
- Homotopy_sphere subject Category:Homotopy_theory.
- Homotopy_sphere subject Category:Topological_spaces.
- Homotopy_sphere hypernym Homotopy.
- Homotopy_sphere type Mapping.
- Homotopy_sphere type Space.
- Homotopy_sphere comment "In algebraic topology, a branch of mathematics, a homotopy sphere is an n-manifold that is homotopy equivalent to the n-sphere.".
- Homotopy_sphere label "Homotopy sphere".
- Homotopy_sphere sameAs m.04gwlm.
- Homotopy_sphere sameAs Q5891833.
- Homotopy_sphere sameAs Q5891833.
- Homotopy_sphere wasDerivedFrom Homotopy_sphere?oldid=620683367.
- Homotopy_sphere isPrimaryTopicOf Homotopy_sphere.