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

Fuente: arXiv
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Autori principali: Domat, George, Hoganson, Hannah, Kwak, Sanghoon
Natura: Preprint
Pubblicazione: 2023
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author Domat, George
Hoganson, Hannah
Kwak, Sanghoon
author_facet Domat, George
Hoganson, Hannah
Kwak, Sanghoon
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2309_07885
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Generating Sets and Algebraic Properties of Pure Mapping Class Groups of Infinite Graphs
Domat, George
Hoganson, Hannah
Kwak, Sanghoon
Group Theory
Geometric Topology
57S05, 37E25, 57M07, 20E08, 20F65, 54H05
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.
title Generating Sets and Algebraic Properties of Pure Mapping Class Groups of Infinite Graphs
topic Group Theory
Geometric Topology
57S05, 37E25, 57M07, 20E08, 20F65, 54H05
url https://arxiv.org/abs/2309.07885