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- 5-manifold abstract "In mathematics, a 5-manifold is a 5-dimensional topological manifold, possibly with a piecewise linear or smooth structure.Non-simply connected 5-manifolds are impossible to classify, as this is harder than solving the word problem for groups. Simply connected compact 5-manifolds were first classified by Dennis Barden and another proof was later given by A. V. Zhubr. Rather surprisingly, this turns out to be easier than the 3- or 4-dimensional case: the 3-dimensional case is the Thurston geometrisation conjecture, and the 4-dimensional case was solved by Freedman (1982) in the topological case, but is a very hard unsolved problem in the smooth case. Indeed, in dimension 5 smooth classification is governed by classical algebraic topology, namely, two simply connected 5-manifolds are diffeomorphic if and only if there exists an isomorphism of their second homology groups with integer coefficients, preserving linking form and the second Stiefel–Whitney class. Moreover any such isomorphism is induced by some diffeomorphism.".
- 5-manifold wikiPageExternalLink 5-manifolds:_1-connected.
- 5-manifold wikiPageID "7763362".
- 5-manifold wikiPageLength "1978".
- 5-manifold wikiPageOutDegree "14".
- 5-manifold wikiPageRevisionID "603129977".
- 5-manifold wikiPageWikiLink 4-manifold.
- 5-manifold wikiPageWikiLink Aleksey_Viktorovich_Zhubr.
- 5-manifold wikiPageWikiLink Category:Geometric_topology.
- 5-manifold wikiPageWikiLink Category:Manifolds.
- 5-manifold wikiPageWikiLink Dennis_Barden.
- 5-manifold wikiPageWikiLink Differential_structure.
- 5-manifold wikiPageWikiLink Geometrization_conjecture.
- 5-manifold wikiPageWikiLink Mathematics.
- 5-manifold wikiPageWikiLink Michael_Freedman.
- 5-manifold wikiPageWikiLink Piecewise_linear_manifold.
- 5-manifold wikiPageWikiLink Piecewise_linear_structure.
- 5-manifold wikiPageWikiLink Simply_connected_space.
- 5-manifold wikiPageWikiLink Stiefel–Whitney_class.
- 5-manifold wikiPageWikiLink Thurston_geometrisation_conjecture.
- 5-manifold wikiPageWikiLink Topological_manifold.
- 5-manifold wikiPageWikiLink Word_problem_for_groups.
- 5-manifold wikiPageWikiLinkText "5-manifold".
- 5-manifold hasPhotoCollection 5-manifold.
- 5-manifold wikiPageUsesTemplate Template:Reflist.
- 5-manifold wikiPageUsesTemplate Template:Topology-stub.
- 5-manifold subject Category:Geometric_topology.
- 5-manifold subject Category:Manifolds.
- 5-manifold type Article.
- 5-manifold type Article.
- 5-manifold type Space.
- 5-manifold comment "In mathematics, a 5-manifold is a 5-dimensional topological manifold, possibly with a piecewise linear or smooth structure.Non-simply connected 5-manifolds are impossible to classify, as this is harder than solving the word problem for groups. Simply connected compact 5-manifolds were first classified by Dennis Barden and another proof was later given by A. V. Zhubr.".
- 5-manifold label "5-manifold".
- 5-manifold sameAs m.026c75d.
- 5-manifold sameAs Q4639668.
- 5-manifold sameAs Q4639668.
- 5-manifold wasDerivedFrom 5-manifold?oldid=603129977.
- 5-manifold isPrimaryTopicOf 5-manifold.