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arXiv · 2506.06538

Non-amenability of mapping class groups of infinite-type surfaces and graphs

Yusen Long
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Abstract

This paper completely determines the non-amenability of the mapping class groups of infinite-type surfaces, the mapping class groups of locally finite infinite graphs of higher ranks, gives an example of non-amenable stabiliser of a point at infinity of a coarsely bounded generated hyperbolic Polish group, and exhibits a class of mapping class groups of trees or rank-one graphs that are amenable.

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Yusen Long. 2025-06-06. Non-amenability of mapping class groups of infinite-type surfaces and graphs. https://arxiv.org/abs/2506.06538

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