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Abstract
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We give a simple proof that any rigid representation of
in
with Euler
number at least
is necessarily semiconjugate to a discrete, faithful representation into
.
Combined with earlier work of Matsumoto, this precisely characterizes Fuchsian actions
by a topological rigidity property. We have proved this result in greater generality, but
with a much more involved proof, in
arxiv:1710.04902.
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Keywords
rigidity, geometricity, Euler class, surface group actions
on the circle
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Mathematical Subject Classification 2010
Primary: 20H10, 37E10, 37E45, 57S25, 58D29
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Milestones
Received: 9 March 2018
Revised: 16 January 2019
Accepted: 21 January 2019
Published: 5 November 2019
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