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The $K(\pi,1)$ conjecture and acylindrical hyperbolicity for relatively extra-large Artin groups

Katherine M Goldman

Algebraic & Geometric Topology 24 (2024) 1487–1504
Abstract

Let AΓ be an Artin group with defining graph Γ. We introduce the notion of AΓ being extra-large relative to a family of arbitrary parabolic subgroups. This generalizes a related notion of AΓ being extra-large relative to two parabolic subgroups, one of which is always large type. Under this new condition, we show that AΓ satisfies the K(π,1) conjecture whenever each of the distinguished subgroups do. In addition, we show that AΓ is acylindrically hyperbolic under only mild conditions.

Keywords
Artin group, Deligne complex, CAT(0), geometric group theory, complex of groups, metric simplicial complex
Mathematical Subject Classification
Primary: 20F36, 20F65
References
Publication
Received: 20 November 2021
Revised: 25 February 2022
Accepted: 17 November 2022
Published: 28 June 2024
Authors
Katherine M Goldman
Department of Mathematics
Ohio State University
Columbus, OH
United States
https://www.asc.ohio-state.edu/goldman.224/

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