C1 actions on the mapping class groups on the circle

Parwani, Kamlesh

doi:10.2140/agt.2008.8.935

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$C^1$ actions on the mapping class groups on the circle

Kamlesh Parwani

Algebraic & Geometric Topology 8 (2008) 935–944

DOI: 10.2140/agt.2008.8.935

Abstract

Let $S$ be a connected orientable surface with finitely many punctures, finitely many boundary components, and genus at least $6$ . Then any $C^{1}$ 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 $C^{1}$ faithful actions on the circle. We also prove that for $n \geq 6$ , any $C^{1}$ action of $Aut (F_{n})$ or $Out (F_{n})$ on the circle factors through an action of $ℤ ∕ 2 ℤ$ .

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

Volume 8, issue 2 (2008)