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- Generalized_Poincaré_conjecture abstract "In the mathematical area of topology, the term Generalized Poincaré conjecture refers to a statement that a manifold which is a homotopy sphere 'is' a sphere. More precisely, one fixes a category of manifolds: topological (Top), piecewise linear (PL), or differentiable (Diff). Then the statement is Every homotopy sphere (a closed n-manifold which is homotopy equivalent to the n-sphere) in the chosen category (i.e. topological manifolds, PL manifolds, or smooth manifolds) is isomorphic in the chosen category (i.e. homeomorphic, PL-isomorphic, or diffeomorphic) to the standard n-sphere.The name derives from the Poincaré conjecture, which was made for (topological or PL) manifolds of dimension 3, where being a homotopy sphere is equivalent to being simply connected. The Generalized Poincaré conjecture is known to be true or false in a number of instances, due to the work of many distinguished topologists, including the Fields medal recipients John Milnor, Steve Smale, Michael Freedman and Grigori Perelman.".
- Generalized_Poincaré_conjecture wikiPageID "8536216".
- Generalized_Poincaré_conjecture wikiPageLength "7646".
- Generalized_Poincaré_conjecture wikiPageOutDegree "39".
- Generalized_Poincaré_conjecture wikiPageRevisionID "619809615".
- Generalized_Poincaré_conjecture wikiPageWikiLink Category:Conjectures.
- Generalized_Poincaré_conjecture wikiPageWikiLink Category:Geometric_topology.
- Generalized_Poincaré_conjecture wikiPageWikiLink Category:Homotopy_theory.
- Generalized_Poincaré_conjecture wikiPageWikiLink Category_(mathematics).
- Generalized_Poincaré_conjecture wikiPageWikiLink Christopher_Zeeman.
- Generalized_Poincaré_conjecture wikiPageWikiLink Clay_Mathematics_Institute.
- Generalized_Poincaré_conjecture wikiPageWikiLink Differentiable_manifold.
- Generalized_Poincaré_conjecture wikiPageWikiLink Differentiable_structure.
- Generalized_Poincaré_conjecture wikiPageWikiLink Differential_structure.
- Generalized_Poincaré_conjecture wikiPageWikiLink Differential_topology.
- Generalized_Poincaré_conjecture wikiPageWikiLink E._C._Zeeman.
- Generalized_Poincaré_conjecture wikiPageWikiLink Exotic_sphere.
- Generalized_Poincaré_conjecture wikiPageWikiLink Fields_Medal.
- Generalized_Poincaré_conjecture wikiPageWikiLink Fields_medal.
- Generalized_Poincaré_conjecture wikiPageWikiLink Gluck_twist.
- Generalized_Poincaré_conjecture wikiPageWikiLink Grigori_Perelman.
- Generalized_Poincaré_conjecture wikiPageWikiLink Homotopy.
- Generalized_Poincaré_conjecture wikiPageWikiLink Homotopy_sphere.
- Generalized_Poincaré_conjecture wikiPageWikiLink John_Milnor.
- Generalized_Poincaré_conjecture wikiPageWikiLink John_R._Stallings.
- Generalized_Poincaré_conjecture wikiPageWikiLink Manifold.
- Generalized_Poincaré_conjecture wikiPageWikiLink Mathematics.
- Generalized_Poincaré_conjecture wikiPageWikiLink Max_Newman.
- Generalized_Poincaré_conjecture wikiPageWikiLink Michael_Freedman.
- Generalized_Poincaré_conjecture wikiPageWikiLink Michel_Kervaire.
- Generalized_Poincaré_conjecture wikiPageWikiLink Millennium_Prize_Problems.
- Generalized_Poincaré_conjecture wikiPageWikiLink Orientability.
- Generalized_Poincaré_conjecture wikiPageWikiLink Piecewise_linear_manifold.
- Generalized_Poincaré_conjecture wikiPageWikiLink Poincaré_conjecture.
- Generalized_Poincaré_conjecture wikiPageWikiLink Simply_connected.
- Generalized_Poincaré_conjecture wikiPageWikiLink Simply_connected_space.
- Generalized_Poincaré_conjecture wikiPageWikiLink Sphere.
- Generalized_Poincaré_conjecture wikiPageWikiLink Stephen_Smale.
- Generalized_Poincaré_conjecture wikiPageWikiLink Steve_Smale.
- Generalized_Poincaré_conjecture wikiPageWikiLink Topological_manifold.
- Generalized_Poincaré_conjecture wikiPageWikiLink Topology.
- Generalized_Poincaré_conjecture wikiPageWikiLinkText "Generalized Poincaré conjecture".
- Generalized_Poincaré_conjecture wikiPageWikiLinkText "Poincaré Conjecture in dimensions greater than six".
- Generalized_Poincaré_conjecture wikiPageWikiLinkText "Poincaré conjecture in dimension four".
- Generalized_Poincaré_conjecture wikiPageWikiLinkText "analogous conjecture".
- Generalized_Poincaré_conjecture wikiPageWikiLinkText "analogous result".
- Generalized_Poincaré_conjecture wikiPageWikiLinkText "analogues of the Poincaré conjecture".
- Generalized_Poincaré_conjecture wikiPageWikiLinkText "generalized Poincaré conjecture".
- Generalized_Poincaré_conjecture wikiPageWikiLinkText "smooth four-dimensional Poincaré conjecture".
- Generalized_Poincaré_conjecture hasPhotoCollection Generalized_Poincaré_conjecture.
- Generalized_Poincaré_conjecture wikiPageUsesTemplate Template:As_of.
- Generalized_Poincaré_conjecture subject Category:Conjectures.
- Generalized_Poincaré_conjecture subject Category:Geometric_topology.
- Generalized_Poincaré_conjecture subject Category:Homotopy_theory.
- Generalized_Poincaré_conjecture comment "In the mathematical area of topology, the term Generalized Poincaré conjecture refers to a statement that a manifold which is a homotopy sphere 'is' a sphere. More precisely, one fixes a category of manifolds: topological (Top), piecewise linear (PL), or differentiable (Diff). Then the statement is Every homotopy sphere (a closed n-manifold which is homotopy equivalent to the n-sphere) in the chosen category (i.e.".
- Generalized_Poincaré_conjecture label "Generalized Poincaré conjecture".
- Generalized_Poincaré_conjecture sameAs m.02770kt.
- Generalized_Poincaré_conjecture sameAs Q5532452.
- Generalized_Poincaré_conjecture sameAs Q5532452.
- Generalized_Poincaré_conjecture wasDerivedFrom Generalized_Poincaré_conjecture?oldid=619809615.
- Generalized_Poincaré_conjecture isPrimaryTopicOf Generalized_Poincaré_conjecture.