Optimal regularity of mapping class group actions on the circle

Abstract: We prove that for each finite index subgroup $H$ of the mapping class group of a closed hyperbolic surface, and for each real number $r>1$ there does not exist a faithful $C^r$-action (in Hölder's sense) of $H$ on a circle. For this, we partially determine the optimal regularity of faithful actions by right-angled Artin groups on a circle. (Joint with Thomas Koberda and Cristobal Rivas)

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

( paper | slides )

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Geometry and topology online

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