Generating Sets and Algebraic Properties of Pure Mapping Class Groups of Infinite Graphs
arXiv (Cornell University)(2023)
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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Key words
pure mapping class groups,infinite,sets
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