The large-scale geometry of a finitely generated group has been well-studied in geometric group theory. But, a big mapping class group, although Polish, is not finitely generated. Christian Rosendal proposed a framework for the large-scale geometry of Polish groups called coarse geometry, see [Ros14]. In recent times, Kathryn Mann and Kasra Rafi studied the large-scale geometry of big mapping class groups using the framework of Rosendal, see [MR20]. We will discuss their papers in this series of talks.



References:


[AV20]     Javier Aramayona and Nicholas G. Vlamis. Big mapping class groups: an overview In In the tradition of Thurston-geometry and topology, pages 459-496. Springer, Cham, [2020] ⓒ2020. (arxiv version)

[MR20]     Kathryn Mann and Kasra Rafi. Large scale geometry of big mapping class groups. arxiv, 2020.


[Ros14]     Christian Rosendal. Large scale geometry of metrisable groups. arxiv, 2014.


[YCV21]     Priyam Patel, Yassin Chandran, and Nicholas G. Vlamis. Infinite-type surfaces and mapping class groups: open problems, 2021.
Coarse geometry, Švarc-Milnor lemma, Non-displaceable subsurface, Self-similar end space
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