Juan Souto, Peter Storm
Published 2005-04-22, updated 2009-02-28Version 3
We study the action of the mapping class group Mod(S) on the boundary dQ of quasifuchsian space Q. Among other results, Mod(S) is shown to be topologically transitive on the subset C in dQ of manifolds without a conformally compact end. We also prove that any open subset of the character variety X(pi_1(S),SL(2,C)) intersecting dQ does not admit a nonconstant Mod(S)-invariant meromorphic function. This is related to a question of Goldman.
Comments: This is the version published by Geometry & Topology on 11 July 2006
Journal: Geom. Topol. 10 (2006) 715-736
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