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Coarsely bounded generating sets for mapping class groups of infinite-type surfaces

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arxiv 2312.02361 v2 pith:7ELWLYTU submitted 2023-12-04 math.GT

Thomas Hill , Sanghoon Kwak , Rebecca Rechkin This is my paper · ORCID
classification math.GT
keywords classgroupsmappinggeneratingsetssurfacesboundedcoarsely
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Mann and Rafi's seminal work initiated the study of the coarse geometry of big mapping class groups. Specifically, they construct coarsely bounded (CB) generating sets for mapping class groups of a large class of infinite-type surfaces. In this expository note, we illustrate examples of surfaces whose mapping class groups admit such generating sets, as well as those that do not, with the goal of exploring the context of Mann--Rafi's hypotheses.

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  1. Graphical models for topological groups: A case study on countable Stone spaces

    math.GR 2024-11 conditional novelty 6.0 of 10

    The paper defines Cayley-Abels-Rosendal graphs for Polish groups and uses them to classify when homeomorphism groups of countable Stone spaces are coarsely bounded, locally bounded, and boundedly generated.

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