How can the answer be improved? nielsen thurston classification The type of an element g of the mapping class group in the Thurston classification is related to its fixed points when acting on the compactification of T ( S ): If g is periodic, then there is a fixed point within T If g is pseudoAnosov, then g has no fixed points in T For some reducible

NielsenThurston 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 ( 1944 ). **nielsen thurston classification**

Fast NielsenThurston classification BalzsStrenner Georgia Institute of Technology (joint with Dan Margalitand ykYurtta) Classification by fixed points on PMF NielsenThurston Classification Mod(S) mapping class group of a surface S Every element of the mapping class group is either Finite order elements fix all of PMF (up to power). U (U) In mathematics, Thurston's classification theorem characterizes homeomorphisms of a compact surface. William Thurston 's theorem completes the work initiated by Jakob Nielsen in the 1930s. Given a homeomorphism f: S S, there is a map g isotopic to f such that either: ALGEBRAIC NIELSENTHURSTON CLASSIFICATION 5. Case with pseudoAnosov component. Suppose is a component of @S0. The maximum number of distinct isotopy classes of disjoint arcs on S0is 3j(S0)j, the number of edges in an ideal triangulation of S0with its boundary shrunk to punctures. *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 NielsenThurston 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 (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 The BirmanHilden Theorem and the NielsenThurston classification. Recall that the BirmanHilden theorem (cf. e. g. Section 9. 4 of Farb and Margalit's wonderful book) defines for us a surjective map: SMod (Sg, 0)Mod (S0, 2g2) with kernel. Here, Sg, n denotes a surface of genus g with n punctures, Mod (S0, 2g2) the mapping class group of S0, 2g2, Another mentioned Thurston's classification theorem for isotopy classes of surface homeomorphisms , not just the title of this article per se. As much as half of them or so refer to the NielsenThurston classification theorem.