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arXiv · 0803.4281

C^1 actions of the mapping class group on the circle

Kamlesh Parwani
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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 > 5, any C^1 action of Aut(F_n) or Out(F_n) on the circle factors through an action of Z/2Z.

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Kamlesh Parwani. 2008-03-29. C^1 actions of the mapping class group on the circle. https://doi.org/10.2140/agt.2008.8.935

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