English

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

Dynamical Systems 2016-01-20 v1 Geometric Topology

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.

Keywords

Cite

@article{arxiv.0803.4281,
  title  = {C^1 actions of the mapping class group on the circle},
  author = {Kamlesh Parwani},
  journal= {arXiv preprint arXiv:0803.4281},
  year   = {2016}
}

Comments

9 pages

R2 v1 2026-06-21T10:25:43.300Z