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

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.

9 pages

References in corpus (2)

• Low-dimensional homology groups of mapping class groups: a survey
• Superrigidity, Weyl groups, and actions on the Circle

Cited by in corpus (8)

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• On the non-realizability of braid groups by diffeomorphisms
• Hyperbolicity as an obstruction to smoothability for one-dimensional actions
• Diffeomorphism groups of critical regularity
• Small $C^1$ actions of semidirect products on compact manifolds
• Actions of right-angled Artin groups in low dimensions
• Mapping class groups of surfaces of genus $\ge 3$ do not virtually surject to $\mathbb{Z}$