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arXiv · 2309.07885

Generating Sets and Algebraic Properties of Pure Mapping Class Groups of Infinite Graphs

George Domat·Hannah Hoganson·Sanghoon Kwak
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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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George Domat, Hannah Hoganson, Sanghoon Kwak. 2023-09-14. Generating Sets and Algebraic Properties of Pure Mapping Class Groups of Infinite Graphs. https://doi.org/10.5802/ahl.238

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