English

Right-angled Artin subgroups of Artin groups

Group Theory 2022-01-19 v2 Geometric Topology

Abstract

The Tits Conjecture, proved by Crisp and Paris, states that squares of the standard generators of any Artin group generate an obvious right-angled Artin subgroup. We consider a larger set of elements consisting of all the centers of the irreducible spherical special subgroups of the Artin group, and conjecture that sufficiently large powers of those elements generate an obvious right-angled Artin subgroup. This alleged right-angled Artin subgroup is in some sense as large as possible; its nerve is homeomorphic to the nerve of the ambient Artin group. We verify this conjecture for the class of locally reducible Artin groups, which includes all 22-dimensional Artin groups, and for spherical Artin groups of any type other than E6E_6, E7E_7, E8E_8. We use our results to conclude that certain Artin groups contain hyperbolic surface subgroups, answering questions of Gordon, Long and Reid.

Keywords

Cite

@article{arxiv.2010.06046,
  title  = {Right-angled Artin subgroups of Artin groups},
  author = {Kasia Jankiewicz and Kevin Schreve},
  journal= {arXiv preprint arXiv:2010.06046},
  year   = {2022}
}

Comments

41 pages, 15 figures. Minor changes to address referee comments. Final version to appear in Journal of the London Mathematical Society