  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.
