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ACYLINDRICAL HYPERBOLICITY OF ARTIN–TITS GROUPS ASSOCIATED WITH TRIANGLE-FREE GRAPHS AND CONES OVER SQUARE-FREE BIPARTITE GRAPHS

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  01 December 2020

MOTOKO KATO  and
SHIN-ICHI OGUNI
MOTOKO KATO
Affiliation:
Graduate School of Science and Engineering, Mathematics, Physics and Earth Sciences, Ehime University, 2-5 Bunkyo-cho, Matsuyama, Ehime 790-8577Japan, e-mails: kato.motoko.yy@ehime-u.ac.jp, oguni.shinichi.mb@ehime-u.ac.jp
SHIN-ICHI OGUNI
Affiliation:
Graduate School of Science and Engineering, Mathematics, Physics and Earth Sciences, Ehime University, 2-5 Bunkyo-cho, Matsuyama, Ehime 790-8577Japan, e-mails: kato.motoko.yy@ehime-u.ac.jp, oguni.shinichi.mb@ehime-u.ac.jp
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Abstract

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It is conjectured that the central quotient of any irreducible Artin–Tits group is either virtually cyclic or acylindrically hyperbolic. We prove this conjecture for Artin–Tits groups that are known to be CAT(0) groups by a result of Brady and McCammond, that is, Artin–Tits groups associated with graphs having no 3-cycles and Artin–Tits groups of almost large type associated with graphs admitting appropriate directions. In particular, the latter family contains Artin–Tits groups of large type associated with cones over square-free bipartite graphs.

MSC classification

Primary: 20F65: Geometric group theory
Secondary: 20F36: Braid groups; Artin groups 20F67: Hyperbolic groups and nonpositively curved groups
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 64 , Issue 1 , January 2022 , pp. 51 - 64
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

Footnotes

†

The first author is supported by JSPS KAKENHI Grant-in-Aid for Research Activity Start-up, Grant Number 19K23406 and JSPS KAKENHI Grant-in-Aid for Young Scientists, Grant Number 20K14311.

‡

The second author is supported by JSPS KAKENHI Grant-in-Aid for Young Scientists (B), Grant Number 16K17595 and 20K03590.

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