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- Homotopy_sphere abstract "In algebraic topology, a branch of mathematics, a homotopy sphere is an n-manifold homotopy equivalent to the n-sphere. It thus has the same homotopy groups and the same homology groups, as the n-sphere. So every homotopy sphere is 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, 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 in such dimensions, homotopy spheres are precisely exotic spheres. It is still an open question whether or not there are non-trivial smooth homotopy spheres in dimension 4.".
- Homotopy_sphere wikiPageID "1202074".
- Homotopy_sphere wikiPageRevisionID "594538853".
- Homotopy_sphere hasPhotoCollection Homotopy_sphere.
- Homotopy_sphere subject Category:Homotopy_theory.
- Homotopy_sphere subject Category:Topological_spaces.
- Homotopy_sphere type Abstraction100002137.
- Homotopy_sphere type Attribute100024264.
- Homotopy_sphere type MathematicalSpace108001685.
- Homotopy_sphere type Set107999699.
- Homotopy_sphere type Space100028651.
- Homotopy_sphere type TopologicalSpaces.
- Homotopy_sphere comment "In algebraic topology, a branch of mathematics, a homotopy sphere is an n-manifold homotopy equivalent to the n-sphere. It thus has the same homotopy groups and the same homology groups, as the n-sphere.".
- Homotopy_sphere label "Homotopy sphere".
- Homotopy_sphere sameAs m.04gwlm.
- Homotopy_sphere sameAs Q5891833.
- Homotopy_sphere sameAs Q5891833.
- Homotopy_sphere sameAs Homotopy_sphere.
- Homotopy_sphere wasDerivedFrom Homotopy_sphere?oldid=594538853.
- Homotopy_sphere isPrimaryTopicOf Homotopy_sphere.