Square complexes and simplicial nonpositive curvature

2011/07/21 by Tomasz Elsner, Elsner, Tomasz, Piotr Przytycki +1
Mathematics · #20F65 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR #math.GT #msc:20F65

paper · pdf · doi:10.48550/arxiv.1107.4182

10 pages, 5 figures

arxiv created 2011/07/21 · openalex publication_date 2011/07/21 · arxiv updated 2011/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that each nonpositively curved square VH-complex can be turned functorially into a locally 6-large simplicial complex of the same homotopy type. It follows that any group acting geometrically on a CAT(0) square VH-complex is systolic. In particular the product of two finitely generated free groups is systolic, which answers a question of Daniel Wise. On the other hand, we exhibit an example of a compact non-VH nonpositively curved square complex, whose fundamental group is neither systolic, nor even virtually systolic.

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