Geometry & Topology 10 (2006) 715–736

DOI: 10.2140/gt.2006.10.715

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),SL₂C) 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

Primary: 57M50

Secondary: 58D27

References

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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