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Hyperbolic Mapping Classes and Their Lifts on the Bers Fiber Space

Authors:	Chaohui ZHANG

Institution:	Department of Mathematical Sciences, Morehouse College, Atlanta, GA 30314, USA

Abstract:	Abstract Let S be a Riemann surface with genus p and n punctures. Assume that 3p−3+n > 0 and n ≥ 1. Let a be a puncture of S and let $\ifmmode\expandafter\tilde\else\expandafter\~\fi{S} = S \cup {\left\{ a \right\}}$ . Then all mapping classes in the mapping class group Mod_S that fixes the puncture a can be projected to mapping classes of ${\text{Mod}}_{{ \ifmmode\expandafter\tilde\else\expandafter\~\fi{S}}}$ under the forgetful map. In this paper the author studies the mapping classes in Mod_S that can be projected to a given hyperbolic mapping class in ${\text{Mod}}_{{ \ifmmode\expandafter\tilde\else\expandafter\~\fi{S}}}$ .

Keywords:	Riemann surfaces Mapping classes Bers fiber spaces
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