On the finiteness property of hyperbolic simplicial actions: the right-angled Artin groups and their extension graphs

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We study the right-angled Artin group action on the extension graph. We show that this action satisfies a certain finiteness property, which is a variation of a condition introduced by Delzant and Bowditch. As an application we show that the asymptotic translation lengths of elements of a given right-angled Artin group are always rational and once the defining graph has girth at least 6, they have a common denominator. We construct explicit examples which show the denominator of the asymptotic translation length of such an action can be arbitrary. We also observe that if either an element has a small syllable length or the defining graph for the right-angled Artin group is a tree then the asymptotic translation lengths are integers.
Publisher
SPRINGER
Issue Date
2023-02
Language
English
Article Type
Article
Citation

GEOMETRIAE DEDICATA, v.217, no.1

ISSN
0046-5755
DOI
10.1007/s10711-022-00736-0
URI
http://hdl.handle.net/10203/300489
Appears in Collection
MA-Journal Papers(저널논문)
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