2024/05/08 by Christopher H. Cashen, Cashen, Christopher H., Alexandra Edletzberger +1
Mathematics · #20F55 #20F65 #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2405.04817
openalex publication_date 2024/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
There is a procedure, due to Dani and Levcovitz, for taking a finite simplicial graph (Γ) and a subgraph (Λ) of its complement, checking some conditions, and, if satisfied, producing a graph (Δ) such that the right-angled Artin group with presentation graph (Δ) is a finite index subgroup of the right-angled Coxeter group with presentation graph (Γ). They do not tell us how to find (Λ), given (Γ). We show, in the 2--dimensional case, that the existence of such a (Λ) is connected to the graph property of satellite-dismantlabilty of (Γ), and we use this to give an algorithm for producing a suitable (Λ) or deciding that one does not exist.