Weak Modularity and \widetildeA_n Buildings

2019/06/24 by Zachary Munro, Munro, Zachary
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1906.10259

openalex publication_date 2019/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The \widetildeA_n Coxeter groups are known to not be systolic or cocompactly cubulated for n≥ 3. We prove that these groups act geometrically on weakly modular graphs, a weak notion of nonpositive curvature generalizing the 1-skeleta of CAT(0) cube complexes and systolic complexes. To prove weak modularity we describe the canonical emeddings of the 1-skeleta of \widetildeA_n Coxeter complexes into the Euclidean spaces ℝⁿ⁺¹. We also prove weak modularity for buildings of type \widetildeA₃.

Citations

• The (2,4,5) Triangle Coxeter Group is not systolic

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