DBpedia – Linked Data Fragments

Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Virtually_fibered_conjecture> ?p ?o }

• Virtually_fibered_conjecture abstract "In the mathematical subfield of 3-manifolds, the virtually fibered conjecture, formulated by American mathematician William Thurston, states that every closed, irreducible, atoroidal 3-manifold with infinite fundamental group has a finite cover which is a surface bundle over the circle. A 3-manifold which has such a finite cover is said to virtually fiber. If M is a Seifert fiber space, then M virtually fibers if and only if the rational Euler number of the Seifert fibration or the (orbifold) Euler characteristic of the base space is zero. The hypotheses of the conjecture are satisfied by hyperbolic 3-manifolds. In fact, given that the geometrization conjecture is now settled, the only case needed to be proven for the virtually fibered conjecture is that of hyperbolic 3-manifolds. The original interest in the virtually fibered conjecture (as well as its weaker cousins, such as the virtually Haken conjecture) stemmed from the fact that any of these conjectures, combined with Thurston's hyperbolization theorem, would imply the geometrization conjecture. However, in practice all known attacks on the "virtual" conjecture take geometrization as a hypothesis, and rely on the geometric and group-theoretic properties of hyperbolic 3-manifolds.The virtually fibered conjecture was not actually conjectured by Thurston. Rather, he posed it as a question and has stated that it was intended as a challenge (and not meant to indicate he believed it). The conjecture was finally settled in the affirmative in a series of papers from 2009 to 2012.In a posting on the ArXiv on 25 Aug 2009, Daniel Wise implicitly implied (by referring to a then unpublished longer manuscript) that he had proven the conjecture for the case where the 3-manifold is closed, hyperbolic, and Haken. This was followed by a survey article in Electronic Research Announcements in Mathematical Sciences.Several more preprints have followed, including the aforementioned longer manuscript by Wise. In March 2012, during a conference at Institut Henri Poincaré in Paris, Ian Agol announced he could prove the virtually Haken conjecture for closed hyperbolic 3-manifolds . Taken together with Daniel Wise's results, this implies the virtually fibered conjecture for all closed hyperbolic 3-manifolds.".
• Virtually_fibered_conjecture wikiPageID "2823145".
• Virtually_fibered_conjecture wikiPageLength "4141".
• Virtually_fibered_conjecture wikiPageOutDegree "26".
• Virtually_fibered_conjecture wikiPageRevisionID "635053989".
• Virtually_fibered_conjecture wikiPageWikiLink 3-manifold.
• Virtually_fibered_conjecture wikiPageWikiLink Atoroidal.
• Virtually_fibered_conjecture wikiPageWikiLink Category:3-manifolds.
• Virtually_fibered_conjecture wikiPageWikiLink Category:Conjectures.
• Virtually_fibered_conjecture wikiPageWikiLink Closed_manifold.
• Virtually_fibered_conjecture wikiPageWikiLink Covering_space.
• Virtually_fibered_conjecture wikiPageWikiLink Daniel_Wise_(mathematician).
• Virtually_fibered_conjecture wikiPageWikiLink Euler_number.
• Virtually_fibered_conjecture wikiPageWikiLink Fundamental_group.
• Virtually_fibered_conjecture wikiPageWikiLink Geometrization_conjecture.
• Virtually_fibered_conjecture wikiPageWikiLink Hyperbolic_3-manifold.
• Virtually_fibered_conjecture wikiPageWikiLink Hyperbolization_theorem.
• Virtually_fibered_conjecture wikiPageWikiLink Ian_Agol.
• Virtually_fibered_conjecture wikiPageWikiLink Institut_Henri_Poincaré.
• Virtually_fibered_conjecture wikiPageWikiLink Irreducible_manifold.
• Virtually_fibered_conjecture wikiPageWikiLink Mathematician.
• Virtually_fibered_conjecture wikiPageWikiLink Orbifold.
• Virtually_fibered_conjecture wikiPageWikiLink Positive_virtual_Betti_number_conjecture.
• Virtually_fibered_conjecture wikiPageWikiLink Prime_manifold.
• Virtually_fibered_conjecture wikiPageWikiLink Seifert_fiber_space.
• Virtually_fibered_conjecture wikiPageWikiLink Surface_bundle_over_the_circle.
• Virtually_fibered_conjecture wikiPageWikiLink Surface_subgroup_conjecture.
• Virtually_fibered_conjecture wikiPageWikiLink United_States.
• Virtually_fibered_conjecture wikiPageWikiLink Virtually_Haken_conjecture.
• Virtually_fibered_conjecture wikiPageWikiLink William_Thurston.
• Virtually_fibered_conjecture wikiPageWikiLinkText "Virtually fibered conjecture".
• Virtually_fibered_conjecture wikiPageWikiLinkText "virtually fibered conjecture".
• Virtually_fibered_conjecture hasPhotoCollection Virtually_fibered_conjecture.
• Virtually_fibered_conjecture wikiPageUsesTemplate Template:Doi.
• Virtually_fibered_conjecture wikiPageUsesTemplate Template:Reflist.
• Virtually_fibered_conjecture subject Category:3-manifolds.
• Virtually_fibered_conjecture subject Category:Conjectures.
• Virtually_fibered_conjecture hypernym Bundle.
• Virtually_fibered_conjecture type AnatomicalStructure.
• Virtually_fibered_conjecture type Conjecture.
• Virtually_fibered_conjecture type Statement.
• Virtually_fibered_conjecture type Statement.
• Virtually_fibered_conjecture comment "In the mathematical subfield of 3-manifolds, the virtually fibered conjecture, formulated by American mathematician William Thurston, states that every closed, irreducible, atoroidal 3-manifold with infinite fundamental group has a finite cover which is a surface bundle over the circle. A 3-manifold which has such a finite cover is said to virtually fiber.".
• Virtually_fibered_conjecture label "Virtually fibered conjecture".
• Virtually_fibered_conjecture sameAs m.084zd3.
• Virtually_fibered_conjecture sameAs Q7935204.
• Virtually_fibered_conjecture sameAs Q7935204.
• Virtually_fibered_conjecture wasDerivedFrom Virtually_fibered_conjecture?oldid=635053989.
• Virtually_fibered_conjecture isPrimaryTopicOf Virtually_fibered_conjecture.