Volume 8, issue 2 (2008)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
$C^1$ actions on the mapping class groups on the circle

Kamlesh Parwani

Algebraic & Geometric Topology 8 (2008) 935–944
Abstract

Let S be a connected orientable surface with finitely many punctures, finitely many boundary components, and genus at least 6. Then any C1 action of the mapping class group of S on the circle is trivial.

The techniques used in the proof of this result permit us to show that products of Kazhdan groups and certain lattices cannot have C1 faithful actions on the circle. We also prove that for n 6, any C1 action of Aut(Fn) or Out(Fn) on the circle factors through an action of 2.

Keywords
mapping class groups, Kazhdan groups, actions on the circle
Mathematical Subject Classification 2000
Primary: 37E10
Secondary: 57M60
References
Publication
Received: 22 February 2008
Revised: 19 March 2008
Accepted: 28 March 2008
Published: 20 June 2008
Authors
Kamlesh Parwani
Department of Mathematics
Eastern Illinois University
600 Lincoln Avenue
Charleston, IL 61920
USA