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

Published 5 Mar 2020 in math.GT and math.DS | (2003.02440v1)

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.

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