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- Surface_subgroup_conjecture abstract "In mathematics, the surface subgroup conjecture of Friedhelm Waldhausen states that the fundamental group of every closed, irreducible 3-manifold with infinite fundamental group has a surface subgroup. By "surface subgroup" we mean the fundamental group of a closed surface not the 2-sphere. This problem is listed as Problem 3.75 in Robion Kirby's problem list.Assuming the geometrization conjecture, the only open case was that of closed hyperbolic 3-manifolds. A proof of this case was announced in the summer of 2009 by Jeremy Kahn and Vladimir Markovic and outlined in a talk August 4, 2009 at the FRG (Focused Research Group) Conference hosted by the University of Utah. A preprint appeared in the arxiv.org server in October 2009. Their paper was published in the Annals of Mathematics in 2012. In June 2012, Kahn and Markovic were given the Clay Research Awards by the Clay Mathematics Institute at a ceremony in Oxford.".
- Surface_subgroup_conjecture thumbnail Jeremy_Kahn_and_Vladimir_Markovic.jpg?width=300.
- Surface_subgroup_conjecture wikiPageID "4565128".
- Surface_subgroup_conjecture wikiPageLength "1891".
- Surface_subgroup_conjecture wikiPageOutDegree "18".
- Surface_subgroup_conjecture wikiPageRevisionID "679402255".
- Surface_subgroup_conjecture wikiPageWikiLink 3-manifold.
- Surface_subgroup_conjecture wikiPageWikiLink Annals_of_Mathematics.
- Surface_subgroup_conjecture wikiPageWikiLink Category:3-manifolds.
- Surface_subgroup_conjecture wikiPageWikiLink Category:Conjectures.
- Surface_subgroup_conjecture wikiPageWikiLink Clay_Mathematics_Institute.
- Surface_subgroup_conjecture wikiPageWikiLink Clay_Research_Award.
- Surface_subgroup_conjecture wikiPageWikiLink Ehrenpreis_conjecture.
- Surface_subgroup_conjecture wikiPageWikiLink Friedhelm_Waldhausen.
- Surface_subgroup_conjecture wikiPageWikiLink Fundamental_group.
- Surface_subgroup_conjecture wikiPageWikiLink Geometrization_conjecture.
- Surface_subgroup_conjecture wikiPageWikiLink Hyperbolic_3-manifold.
- Surface_subgroup_conjecture wikiPageWikiLink Jeremy_Kahn.
- Surface_subgroup_conjecture wikiPageWikiLink Mathematics.
- Surface_subgroup_conjecture wikiPageWikiLink Oxford.
- Surface_subgroup_conjecture wikiPageWikiLink Robion_Kirby.
- Surface_subgroup_conjecture wikiPageWikiLink Virtually_Haken_conjecture.
- Surface_subgroup_conjecture wikiPageWikiLink Vladimir_Markovic.
- Surface_subgroup_conjecture wikiPageWikiLink File:Jeremy_Kahn_and_Vladimir_Markovic.jpg.
- Surface_subgroup_conjecture wikiPageWikiLinkText "Surface subgroup conjecture ".
- Surface_subgroup_conjecture wikiPageWikiLinkText "Surface subgroup conjecture".
- Surface_subgroup_conjecture wikiPageWikiLinkText "surface subgroup conjecture".
- Surface_subgroup_conjecture hasPhotoCollection Surface_subgroup_conjecture.
- Surface_subgroup_conjecture wikiPageUsesTemplate Template:Reflist.
- Surface_subgroup_conjecture wikiPageUsesTemplate Template:Topology-stub.
- Surface_subgroup_conjecture subject Category:3-manifolds.
- Surface_subgroup_conjecture subject Category:Conjectures.
- Surface_subgroup_conjecture type Article.
- Surface_subgroup_conjecture type Article.
- Surface_subgroup_conjecture type Conjecture.
- Surface_subgroup_conjecture type Statement.
- Surface_subgroup_conjecture type Statement.
- Surface_subgroup_conjecture comment "In mathematics, the surface subgroup conjecture of Friedhelm Waldhausen states that the fundamental group of every closed, irreducible 3-manifold with infinite fundamental group has a surface subgroup. By "surface subgroup" we mean the fundamental group of a closed surface not the 2-sphere. This problem is listed as Problem 3.75 in Robion Kirby's problem list.Assuming the geometrization conjecture, the only open case was that of closed hyperbolic 3-manifolds.".
- Surface_subgroup_conjecture label "Surface subgroup conjecture".
- Surface_subgroup_conjecture sameAs m.0c94d8.
- Surface_subgroup_conjecture sameAs Q7646025.
- Surface_subgroup_conjecture sameAs Q7646025.
- Surface_subgroup_conjecture wasDerivedFrom Surface_subgroup_conjecture?oldid=679402255.
- Surface_subgroup_conjecture depiction Jeremy_Kahn_and_Vladimir_Markovic.jpg.
- Surface_subgroup_conjecture isPrimaryTopicOf Surface_subgroup_conjecture.