Volume 10, issue 2 (2006)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Dynamics of the mapping class group action on the variety of $\mathrm{PSL}_2 \mathbb{C}$ characters

Juan Souto and Peter Storm

Geometry & Topology 10 (2006) 715–736

arXiv: math.GT/0504474

Abstract

We study the action of the mapping class group Mod(S) on the boundary Q of quasifuchsian space Q. Among other results, Mod(S) is shown to be topologically transitive on the subset C Q of manifolds without a conformally compact end. We also prove that any open subset of the character variety X(π1(S),SL2) intersecting Q does not admit a nonconstant Mod(S)–invariant meromorphic function. This is related to a question of Goldman.

Keywords
hyperbolic geometry, mapping class group
Mathematical Subject Classification 2000
Primary: 57M50
Secondary: 58D27
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Publication
Received: 14 January 2006
Accepted: 30 April 2006
Published: 11 July 2006
Proposed: Benson Farb
Seconded: Walter Neumann, Jean-Pierre Otal
Authors
Juan Souto
Department of Mathematics
University of Chicago
5734 University Avenue
Chicago IL 60637-1514
USA
Peter Storm
Department of Mathematics
Stanford University
450 Serra Mall
Stanford CA 94305-2125
USA