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

Goldman, Katherine M

doi:10.2140/agt.2024.24.1487

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

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

Katherine M Goldman

Algebraic & Geometric Topology 24 (2024) 1487–1504

DOI: 10.2140/agt.2024.24.1487

Abstract

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

Open Access made possible by participating institutions via Subscribe to Open.

Volume 24, issue 3 (2024)