Standard Form

Abstract

Given a pseudo-periodic map $f :{\Sigma_g}\rightarrow{\Sigma_g}$ Nielsen constructed a special homeomorphism which is homotopic to f and plays the role of a “standard form” in the mapping class of f , [53, Sect. 14]. In this Chapter, we will construct a similar standard form, slightly different from Nielsen’s, and will show its essential uniqueness. He wanted to avoid fixed points which might appear in annular neighborhoods of cut curves, while we do not care about such fixed points (Compare [22, Theorem 13.3]).