RAAGedy right-angled Coxeter groups
Christopher H. Cashen, Pallavi Dani, Alexandra Edletzberger, Annette Karrer

TL;DR
This paper provides criteria and methods to determine when a triangle-free graph defines a right-angled Coxeter group that is quasiisometric to a right-angled Artin group, introducing new graph operations and computational tools.
Contribution
It introduces new graph modification operations and develops criteria for identifying quasiisometric relationships between Coxeter and Artin groups.
Findings
Criteria for identifying such graphs are established.
New graph operations, cloning and unfolding, are introduced.
The methods are implemented and successfully applied to small graphs.
Abstract
We give criteria for deciding whether or not a triangle-free simple graph is the presentation graph of a right-angled Coxeter group that is quasiisometric to some right-angled Artin group, and, if so, producing a presentation graph for such a right-angled Artin group. We introduce two new graph modification operations, cloning and unfolding, to go along with an existing operation called link doubling. These operations change the presentation graph but not the quasiisometry type of the resulting group. We give criteria on the graph that imply it can be transformed by these operations into a graph that is recognizable as presenting a right-angled Coxeter group commensurable to a right-angled Artin group. In the converse direction we derive coarse geometric obstructions to being quasiisometric to a right-angled Artin group, first by specializing existing results from the literature to…
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology
