A note on almost negative matrices and Gromov-hyperbolic Coxeter groups

2022/05/16 by Philip Möller, Möller, Philip
Mathematics · #20F55 (primary) #51F15(secondary) #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2205.07791

openalex publication_date 2022/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this note we revisit Moussong's Characterization of Gromov-hyperbolic Coxeter groups. A Coxeter group is Gromov-hyperbolic if and only if it does not contain a subgroup isomorphic to ℤ² which can be read off directly from the defining graph. We show that there is a small gap in the original argument and provide a workaround.

Related

• Relative hyperbolicity and right-angled Coxeter groups
• A construction of hyperbolic Coxeter groups
• A brief introduction to Gromov's notion of hyperbolic groups
• On definitions of relatively hyperbolic groups
• A decomposition theorem for higher rank Coxeter groups