Algebraic & Geometric Topology

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

Kamlesh Parwani

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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 n6, any C1 action of Aut(Fn) or Out(Fn) on the circle factors through an action of 2.

Article information

Algebr. Geom. Topol., Volume 8, Number 2 (2008), 935-944.

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 37E10: Maps of the circle
Secondary: 57M60: Group actions in low dimensions

mapping class groups Kazhdan groups actions on the circle


Parwani, Kamlesh. $C^1$ actions on the mapping class groups on the circle. Algebr. Geom. Topol. 8 (2008), no. 2, 935--944. doi:10.2140/agt.2008.8.935.

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