The virtual critical regularity of mapping class group actions on a circle


We prove that for each finite index subgroup H of the mapping class group of a closed hyperbolic surface, and for each real number r larger than one, there does not exist a faithful C-r-action (in Hölder’s sense) of H on a circle. For this, we partially determine the critical regularity of faithful actions by right-angled Artin groups on a circle. (Joint with Thomas Koberda and Cristobal Rivas)