C¹ actions of the mapping class group on the circle

2008/03/29 by Kamlesh Parwani · 1 citation
Mathematics · #math.DS #math.GT #msc:37E10

paper · pdf · doi:10.2140/agt.2008.8.935

published as Algebr. Geom. Topol. 8 (2008) 935-944 · 9 pages

arxiv created 2008/03/29 · arxiv updated 2016/01/20

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(F_n) or Out(F_n) on the circle factors through an action of Z/2Z.

Cited by

• C¹ actions on the circle of finite index subgroups of Mod(Σ_g), Aut(F_n), and Out(F_n)