Cayley-Abels graphs: Local and global perspectives

Waltraud Lederle

Cayley-Abels graphs: Local and global perspectives

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arxiv 2210.16284 v1 pith:25E36LWX submitted 2022-10-28 math.GR

Waltraud Lederle This is my paper · ORCID

classification math.GR

keywords cayley-abelsgeneratedgroupsfinitelygraphgraphshandtdlc

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We give an introduction to the Cayley-Abels graph for a totally disconnected, locally compact (tdlc) group. It is a generalization of the Cayley graph. We illustrate that on the one hand, Cayley-Abels graphs are useful tools to extend concepts concerning finitely generated groups to compactly generated, tdlc groups and on the other hand, they can be used to investigate properties that, for finitely generated groups, are trivial.

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Graphical models for topological groups: A case study on countable Stone spaces
math.GR 2024-11 conditional novelty 6.0 of 10

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.

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