August 11, 2025Open Access

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

Key Points

The classification shows pure mapping class groups of certain infinite graphs have coarsely bounded generating sets, indicating structure.
A semidirect product decomposition is established, providing insights into their algebraic properties within the domain.
First integral cohomology computations inform on the group structure, enhancing understanding of topological applications.
Findings imply implications for quasi-isometric and algebraic rigidity, expanding on properties like residual finiteness and the Tits alternative.

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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Cite This Study

Domat et al. (Thu,) studied this question.

synapsesocial.com/papers/68a35efb0a429f7973328782 https://doi.org/https://doi.org/10.5802/ahl.238

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