Non-realizability of some big mapping class groups

Chen, Lei; He, Yan Mary

doi:10.1090/proc/16860

Non-realizability of some big mapping class groups
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by Lei Chen and Yan Mary He;

Proc. Amer. Math. Soc. 152 (2024), 4503-4514

DOI: https://doi.org/10.1090/proc/16860

Published electronically: August 26, 2024

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Abstract:

In this note, we prove that the compactly supported mapping class group of a surface containing a genus $3$ subsurface has no realization as a subgroup of the homeomorphism group. We also prove that for certain surfaces with order $6$ 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.

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