C1 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 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 n > 5, any C1 action of Aut(Fn) or Out(Fn) on the circle factors through an action of Z/2Z.
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