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2008 $C^1$ actions on the mapping class groups on the circle
Kamlesh Parwani
Algebr. Geom. Topol. 8(2): 935-944 (2008). 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 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 n6, any C1 action of Aut(Fn) or Out(Fn) on the circle factors through an action of 2.

Citation

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Kamlesh Parwani. "$C^1$ actions on the mapping class groups on the circle." Algebr. Geom. Topol. 8 (2) 935 - 944, 2008. https://doi.org/10.2140/agt.2008.8.935

Information

Received: 22 February 2008; Revised: 19 March 2008; Accepted: 28 March 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1155.37028
MathSciNet: MR2443102
Digital Object Identifier: 10.2140/agt.2008.8.935

Subjects:
Primary: 37E10
Secondary: 57M60

Rights: Copyright © 2008 Mathematical Sciences Publishers

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