Classifying spaces for families of subgroups of 8-located groups

2021/01/03 by Ioana‐Claudia Lazăr, Lazăr, Ioana-Claudia
Computer Science · Mathematics · #05C99 #20F67 #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2101.00581

openalex publication_date 2021/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the structure of the minimal displacement set in 8-located complexes with the SD'-property. We show that such set embeds isometrically into the complex. Since 8-location and simple connectivity imply Gromov hyperbolicity, the minimal displacement set in such complex is systolic. Using these results, we construct a low-dimensional classifying space for the family of virtually cyclic subgroups of a group acting properly on an 8-located complex with the SD'-property.

Citations

• A combinatorial non-positive curvature I: weak systolicity
• A combinatorial negative curvature condition implying Gromov\n hyperbolicity

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• Survey on Classifying Spaces for Families of Subgroups
• On the classifying space of the family of virtually cyclic subgroups
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