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- Nielsen–Thurston_classification abstract "In mathematics, Thurston's classification theorem characterizes homeomorphisms of a compact orientable surface. William Thurston's theorem completes the work initiated by Jakob Nielsen (1944).Given a homeomorphism f : S → S, there is a map g isotopic to f such that at least one of the following holds: g is periodic, i.e. some power of g is the identity; g preserves some finite union of disjoint simple closed curves on S (in this case, g is called reducible); or g is pseudo-Anosov.The case where S is a torus (i.e., a surface whose genus is one) is handled separately (see torus bundle) and was known before Thurston's work. If the genus of S is two or greater, then S is naturally hyperbolic, and the tools of Teichmüller theory become useful. In what follows, we assume S has genus at least two, as this is the case Thurston considered. (Note, however, that the cases where S has boundary or is not orientable are definitely still of interest.)The three types in this classification are not mutually exclusive, though a pseudo-Anosov homeomorphism is never periodic or reducible. A reducible homeomorphism g can be further analyzed by cutting the surface along the preserved union of simple closed curves Γ. Each of the resulting compact surfaces with boundary is acted upon by some power (i.e. iterated composition) of g, and the classification can again be applied to this homeomorphism.".
- Nielsen–Thurston_classification wikiPageID "1684758".
- Nielsen–Thurston_classification wikiPageLength "7776".
- Nielsen–Thurston_classification wikiPageOutDegree "58".
- Nielsen–Thurston_classification wikiPageRevisionID "700972267".
- Nielsen–Thurston_classification wikiPageWikiLink 3-manifold.
- Nielsen–Thurston_classification wikiPageWikiLink Boundary_(topology).
- Nielsen–Thurston_classification wikiPageWikiLink Canonical_form.
- Nielsen–Thurston_classification wikiPageWikiLink Category:Geometric_topology.
- Nielsen–Thurston_classification wikiPageWikiLink Category:Homeomorphisms.
- Nielsen–Thurston_classification wikiPageWikiLink Category:Surfaces.
- Nielsen–Thurston_classification wikiPageWikiLink Category:Theorems_in_topology.
- Nielsen–Thurston_classification wikiPageWikiLink Closed_manifold.
- Nielsen–Thurston_classification wikiPageWikiLink Compactification_(mathematics).
- Nielsen–Thurston_classification wikiPageWikiLink Dehn_twist.
- Nielsen–Thurston_classification wikiPageWikiLink Dynamical_system.
- Nielsen–Thurston_classification wikiPageWikiLink Foliation.
- Nielsen–Thurston_classification wikiPageWikiLink Function_composition.
- Nielsen–Thurston_classification wikiPageWikiLink Genus.
- Nielsen–Thurston_classification wikiPageWikiLink Geometrization_conjecture.
- Nielsen–Thurston_classification wikiPageWikiLink Haken_manifold.
- Nielsen–Thurston_classification wikiPageWikiLink Homeomorphism.
- Nielsen–Thurston_classification wikiPageWikiLink Homotopy.
- Nielsen–Thurston_classification wikiPageWikiLink Hyperbolic_geometry.
- Nielsen–Thurston_classification wikiPageWikiLink Incompressible_surface.
- Nielsen–Thurston_classification wikiPageWikiLink Isometry.
- Nielsen–Thurston_classification wikiPageWikiLink Isometry_group.
- Nielsen–Thurston_classification wikiPageWikiLink JSJ_decomposition.
- Nielsen–Thurston_classification wikiPageWikiLink Jakob_Nielsen_(mathematician).
- Nielsen–Thurston_classification wikiPageWikiLink Kleinian_group.
- Nielsen–Thurston_classification wikiPageWikiLink Limit_set.
- Nielsen–Thurston_classification wikiPageWikiLink Manifold.
- Nielsen–Thurston_classification wikiPageWikiLink Mapping_class_group.
- Nielsen–Thurston_classification wikiPageWikiLink Mapping_torus.
- Nielsen–Thurston_classification wikiPageWikiLink Mathematics.
- Nielsen–Thurston_classification wikiPageWikiLink Mladen_Bestvina.
- Nielsen–Thurston_classification wikiPageWikiLink Orientability.
- Nielsen–Thurston_classification wikiPageWikiLink Pants_decomposition.
- Nielsen–Thurston_classification wikiPageWikiLink Pseudo-Anosov_map.
- Nielsen–Thurston_classification wikiPageWikiLink Reduction_(mathematics).
- Nielsen–Thurston_classification wikiPageWikiLink Space-filling_curve.
- Nielsen–Thurston_classification wikiPageWikiLink Surface_bundle_over_the_circle.
- Nielsen–Thurston_classification wikiPageWikiLink Teichmüller_space.
- Nielsen–Thurston_classification wikiPageWikiLink Torus.
- Nielsen–Thurston_classification wikiPageWikiLink Torus_bundle.
- Nielsen–Thurston_classification wikiPageWikiLink Train_track_map.
- Nielsen–Thurston_classification wikiPageWikiLink Transversality_(mathematics).
- Nielsen–Thurston_classification wikiPageWikiLink Werner_Fenchel.
- Nielsen–Thurston_classification wikiPageWikiLink William_Thurston.
- Nielsen–Thurston_classification wikiPageWikiLinkText "Nielsen–Thurston classification".
- Nielsen–Thurston_classification wikiPageWikiLinkText "Thurston–Nielsen classification".
- Nielsen–Thurston_classification wikiPageWikiLinkText "classification of diffeomorphisms of a surface".
- Nielsen–Thurston_classification authorlink "Jakob Nielsen".
- Nielsen–Thurston_classification first "Jakob".
- Nielsen–Thurston_classification last "Nielsen".
- Nielsen–Thurston_classification wikiPageUsesTemplate Template:Citation.
- Nielsen–Thurston_classification wikiPageUsesTemplate Template:Cite_book.
- Nielsen–Thurston_classification wikiPageUsesTemplate Template:Harvs.
- Nielsen–Thurston_classification year "1944".
- Nielsen–Thurston_classification subject Category:Geometric_topology.
- Nielsen–Thurston_classification subject Category:Homeomorphisms.
- Nielsen–Thurston_classification subject Category:Surfaces.
- Nielsen–Thurston_classification subject Category:Theorems_in_topology.
- Nielsen–Thurston_classification type Homeomorphism.
- Nielsen–Thurston_classification type Mapping.
- Nielsen–Thurston_classification type Morphism.
- Nielsen–Thurston_classification type Redirect.
- Nielsen–Thurston_classification type Surface.
- Nielsen–Thurston_classification type Theorem.
- Nielsen–Thurston_classification comment "In mathematics, Thurston's classification theorem characterizes homeomorphisms of a compact orientable surface. William Thurston's theorem completes the work initiated by Jakob Nielsen (1944).Given a homeomorphism f : S → S, there is a map g isotopic to f such that at least one of the following holds: g is periodic, i.e.".
- Nielsen–Thurston_classification label "Nielsen–Thurston classification".
- Nielsen–Thurston_classification sameAs Q7031628.
- Nielsen–Thurston_classification sameAs m.05n71x.
- Nielsen–Thurston_classification sameAs Q7031628.
- Nielsen–Thurston_classification wasDerivedFrom Nielsen–Thurston_classification?oldid=700972267.
- Nielsen–Thurston_classification isPrimaryTopicOf Nielsen–Thurston_classification.