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G&T Monographs |
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Dynamics of the mapping class group action on the variety
of PSL2 C characters
Juan Souto and Peter Storm
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Geometry & Topology 10 (2006)
715–736
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Abstract
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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.
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Keywords
hyperbolic geometry, mapping class
group
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Mathematical Subject Classification
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
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