Download this article
 Download this article For screen
For printing
Recent Issues

Volume 24
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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
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/

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