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- Haken_manifold abstract "In mathematics, a Haken manifold is a compact, P²-irreducible 3-manifold that is sufficiently large, meaning that it contains a properly embedded two-sided incompressible surface. Sometimes one considers only orientable Haken manifolds, in which case a Haken manifold is a compact, orientable, irreducible 3-manifold that contains an orientable, incompressible surface.A 3-manifold finitely covered by a Haken manifold is said to be virtually Haken. The Virtually Haken conjecture asserts that every compact, irreducible 3-manifold with infinite fundamental group is virtually Haken.Haken manifolds were introduced by Haken (1961). Haken (1962) proved that Haken manifolds have a hierarchy, where they can be split up into 3-balls along incompressible surfaces. Haken also showed that there was a finite procedure to find an incompressible surface if the 3-manifold had one. Jaco & Oertel (1984) gave an algorithm to determine if a 3-manifold was Haken.Normal surfaces are ubiquitous in the theory of Haken manifolds and their simple and rigid structure leads quite naturally to algorithms.".
- Haken_manifold wikiPageExternalLink books?id=Tf4-AAAAIAAJ.
- Haken_manifold wikiPageID "236567".
- Haken_manifold wikiPageLength "6914".
- Haken_manifold wikiPageOutDegree "31".
- Haken_manifold wikiPageRevisionID "689769338".
- Haken_manifold wikiPageWikiLink 2-sided.
- Haken_manifold wikiPageWikiLink 3-manifold.
- Haken_manifold wikiPageWikiLink Acta_Mathematica.
- Haken_manifold wikiPageWikiLink Annals_of_Mathematics.
- Haken_manifold wikiPageWikiLink Atoroidal.
- Haken_manifold wikiPageWikiLink Betti_number.
- Haken_manifold wikiPageWikiLink Category:3-manifolds.
- Haken_manifold wikiPageWikiLink Compact_space.
- Haken_manifold wikiPageWikiLink Hyperbolization_theorem.
- Haken_manifold wikiPageWikiLink I-bundle.
- Haken_manifold wikiPageWikiLink Incompressible_surface.
- Haken_manifold wikiPageWikiLink Knot_complement.
- Haken_manifold wikiPageWikiLink Manifold_decomposition.
- Haken_manifold wikiPageWikiLink Mapping_class_group.
- Haken_manifold wikiPageWikiLink Mathematics.
- Haken_manifold wikiPageWikiLink Mathematische_Zeitschrift.
- Haken_manifold wikiPageWikiLink Mostow_rigidity_theorem.
- Haken_manifold wikiPageWikiLink Normal_surface.
- Haken_manifold wikiPageWikiLink Orientability.
- Haken_manifold wikiPageWikiLink P2-irreducible_manifold.
- Haken_manifold wikiPageWikiLink Princeton_University_Press.
- Haken_manifold wikiPageWikiLink Regular_neighborhood.
- Haken_manifold wikiPageWikiLink Seifert_fiber_space.
- Haken_manifold wikiPageWikiLink Springer_Science+Business_Media.
- Haken_manifold wikiPageWikiLink Surface_bundle_over_the_circle.
- Haken_manifold wikiPageWikiLink Topological_rigidity.
- Haken_manifold wikiPageWikiLink Topology_(journal).
- Haken_manifold wikiPageWikiLink Virtually_Haken_conjecture.
- Haken_manifold wikiPageWikiLink William_Thurston.
- Haken_manifold wikiPageWikiLinkText "Haken 3-manifolds".
- Haken_manifold wikiPageWikiLinkText "Haken manifold".
- Haken_manifold wikiPageWikiLinkText "Haken".
- Haken_manifold wikiPageWikiLinkText "Haken_manifold".
- Haken_manifold wikiPageUsesTemplate Template:Citation.
- Haken_manifold wikiPageUsesTemplate Template:Harvs.
- Haken_manifold wikiPageUsesTemplate Template:Harvtxt.
- Haken_manifold subject Category:3-manifolds.
- Haken_manifold hypernym Compact.
- Haken_manifold type Weapon.
- Haken_manifold comment "In mathematics, a Haken manifold is a compact, P²-irreducible 3-manifold that is sufficiently large, meaning that it contains a properly embedded two-sided incompressible surface. Sometimes one considers only orientable Haken manifolds, in which case a Haken manifold is a compact, orientable, irreducible 3-manifold that contains an orientable, incompressible surface.A 3-manifold finitely covered by a Haken manifold is said to be virtually Haken.".
- Haken_manifold label "Haken manifold".
- Haken_manifold sameAs Q2589609.
- Haken_manifold sameAs Haken-Mannigfaltigkeit.
- Haken_manifold sameAs Haken-variëteit.
- Haken_manifold sameAs m.01jbm6.
- Haken_manifold sameAs Q2589609.
- Haken_manifold wasDerivedFrom Haken_manifold?oldid=689769338.
- Haken_manifold isPrimaryTopicOf Haken_manifold.