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 ≥ 6, any
C1 action of Aut(Fn) or Out(Fn) on the
circle factors through an action of Z/2Z.