Quasi-isometry invariants of weakly special square complexes
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Publication:6348694
DOI10.1016/J.TOPOL.2021.107945arXiv2009.03865MaRDI QIDQ6348694
Publication date: 8 September 2020
Abstract: We define the intersection complex for the universal cover of a compact weakly special square complex and show that it is a quasi-isometry invariant. By using this quasi-isometry invariant, we study the quasi-isometric classification of 2-dimensional right-angled Artin groups and planar graph 2-braid groups. Our results cover two well-known cases of 2-dimensional right-angled Artin groups: (1) those whose defining graphs are trees and (2) those whose outer automorphism groups are finite. Finally, we show that there are infinitely many graph 2-braid groups which are quasi-isometric to right-angled Artin groups and infinitely many which are not.
Geometric group theory (20F65) Braid groups; Artin groups (20F36) Topological methods in group theory (57M07) Hyperbolic groups and nonpositively curved groups (20F67)
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