Virtual critical regularity of mapping class group actions on the circle

2021/04/30 by Sang-hyun Kim, Thomas Koberda, Kim, Sang-hyun +3
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.DS #math.GR #math.GT

paper · pdf · doi:10.48550/arxiv.2104.15073

11 pages, to appear in Transformation Groups

arxiv created 2022/01/19 · arxiv updated 2022/01/21

Abstract

We show that if G₁ and G₂ are non-solvable groups, then no C^1,τ action of (G₁× G₂)*ℤ on S¹ is faithful for τ>0. As a corollary, if S is an orientable surface of complexity at least three then the critical regularity of an arbitrary finite index subgroup of the mapping class group Mod(S) with respect to the circle is at most one, thus strengthening a result of the first two authors with Baik.

Related

• Direct products, overlapping actions, and critical regularity
• Structure and regularity of group actions on one-manifolds
• Exotic mapping class group actions on the circle
• C¹ actions on the circle of finite index subgroups of Mod(Σ_g), Aut(F_n), and Out(F_n)
• Diffeomorphism groups of critical regularity