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arXiv · 2405.04817

Visual right-angled Artin subgroups of two-dimensional right-angled Coxeter groups

Christopher H. Cashen·Alexandra Edletzberger
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Abstract

There is a procedure, due to Dani and Levcovitz, for taking a finite simplicial graph (\Gamma) and a subgraph (\Lambda) of its complement, checking some conditions, and, if satisfied, producing a graph (\Delta) such that the right-angled Artin group with presentation graph (\Delta) is a finite index subgroup of the right-angled Coxeter group with presentation graph (\Gamma). They do not tell us how to find (\Lambda), given (\Gamma). We show, in the 2--dimensional case, that the existence of such a (\Lambda) is connected to the graph property of satellite-dismantlabilty of (\Gamma), and we use this to give an algorithm for producing a suitable (\Lambda) or deciding that one does not exist.

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Christopher H. Cashen, Alexandra Edletzberger. 2024-05-08. Visual right-angled Artin subgroups of two-dimensional right-angled Coxeter groups. https://doi.org/10.1515/jgth-2024-0109

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