Non-realizability of some big mapping class groups

Author:

Chen Lei,He Yan Mary

Abstract

In this note, we prove that the compactly supported mapping class group of a surface containing a genus 3 3 subsurface has no realization as a subgroup of the homeomorphism group. We also prove that for certain surfaces with order 6 6 symmetries, their mapping class groups have no realization as a subgroup of the homeomorphism group. Examples of such surfaces include the plane minus a Cantor set and the sphere minus a Cantor set.

Funder

National Science Foundation

Publisher

American Mathematical Society (AMS)

Reference17 articles.

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5. Big mapping class groups and rigidity of the simple circle;Calegari, Danny;Ergodic Theory Dynam. Systems,2021

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