Pseudo-Anosov mapping classes and their representations by products of two Dehn twists

Abstract

Let $\tilde S$ be a Riemann surface of analytically finite type (p, n) with 3p − 3 + n > 0. Let a ∈ $\tilde S$ and S = $\tilde S$ − {a}. In this article, the author studies those pseudo-Anosov maps on S that are isotopic to the identity on $\tilde S$ and can be represented by products of Dehn twists. It is also proved that for any pseudo-Anosov map f of S isotopic to the identity on $\tilde S$, there are infinitely many pseudo-Anosov maps F on S − {b} = $\tilde S$ − {a, b}, where b is a point on S, such that F is isotopic to f on S as b is filled in.

Keywords

Riemann surface / Pseudo-Anosov map / Dehn twist / Teichmüller space / Bers fiber space

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