Nielsen–Thurston classification

In mathematics, Thurston's classification theorem characterizes homeomorphisms of a compact orientable surface. William Thurston's theorem completes the work initiated by Jakob Nielsen . 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.

Nielsen–Thurston classification

In mathematics, Thurston's classification theorem characterizes homeomorphisms of a compact orientable surface. William Thurston's theorem completes the work initiated by Jakob Nielsen . 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.