Global fixed points of mapping class group actions and a theorem of Markovic

2020/03/05 by Chen, Lei, Salter, Nick
#Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2003.02440

Abstract

We give a short and elementary proof of the non-realizability of the mapping class group via homeomorphisms. This was originally established by Markovic, resolving a conjecture of Thurston. With the tools established in this paper, we also obtain some rigidity results for actions of the mapping class group on Euclidean spaces.

Related

• Actions of mapping class groups
• Exotic mapping class group actions on the circle
• Non-realizability of some big mapping class groups
• The Farrell-Jones Conjecture for mapping class groups
• Homomorphisms from mapping class groups