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.
Generating Sets and Algebraic Properties of Pure Mapping Class Groups of Infinite Graphs
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abstract
We completely classify the locally finite, infinite graphs with pure mapping class groups admitting a coarsely bounded generating set. We also study algebraic properties of the pure mapping class group: We establish a semidirect product decomposition, compute first integral cohomology, and classify when they satisfy residual finiteness and the Tits alternative. These results provide a framework and some initial steps towards quasi-isometric and algebraic rigidity of these groups.
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math.GR 1years
2024 1verdicts
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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.