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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 wikiPageRevisionID "551263375".
- Nielsen–Thurston_classification authorlink "Jakob Nielsen".
- Nielsen–Thurston_classification first "Jakob".
- Nielsen–Thurston_classification last "Nielsen".
- 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 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 Nielsen%E2%80%93Thurston_classification.
- Nielsen–Thurston_classification sameAs Q7031628.
- Nielsen–Thurston_classification sameAs Q7031628.
- Nielsen–Thurston_classification wasDerivedFrom Nielsen–Thurston_classification?oldid=551263375.