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.
Large scale geometry of B anach- L ie groups
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Graphical models for topological groups: A case study on countable Stone spaces
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.