Dynamics of the mapping class group action on the variety of PSL(2,C) characters

Details Dynamics of the mapping class group action on the variety of PSL(2,C) characters Dynamics of the mapping class group action on the variety of PSL(2,C) characters

2005-04-22

arxiv.org/abs/math/0504474v3

Geom. Topol. 10 (2006) 715-736

Mathematics

Geometric Topology

This is the version published by Geometry & Topology on 11 July 2006

Scientific paper

10.2140/gt.2006.10.715

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.

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