Geodesic
C1 actions on the mapping class groups on the circle
Parwani, Kamlesh1
1Department of Mathematics, Eastern Illinois University, 600 Lincoln Avenue, Charleston, IL 61920, USA
Algebraic and Geometric Topology, Tome 8 (2008) no. 2, pp. 935-944
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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 ℤ∕2ℤ.

DOI : 10.2140/agt.2008.8.935
Keywords: mapping class groups, Kazhdan groups, actions on the circle

Parwani, Kamlesh  1

1 Department of Mathematics, Eastern Illinois University, 600 Lincoln Avenue, Charleston, IL 61920, USA 
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Parwani, Kamlesh. C1 actions on the mapping class groups on the circle. Algebraic and Geometric Topology, Tome 8 (2008) no. 2, pp. 935-944. doi: 10.2140/agt.2008.8.935

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