Large-type Artin groups are systolic
Abstract
We prove that Artin groups from a class containing all large-type Artin groups are systolic. This provides a concise yet precise description of their geometry. Immediate consequences are new results concerning large-type Artin groups: biautomaticity; existence of $EZ$-boundaries; the Novikov conjecture; descriptions of finitely presented subgroups, of virtually solvable subgroups, and of centralizers for infinite order elements; the Burghelea conjecture; existence of low-dimensional models for classifying spaces for some families of subgroups.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2017
- DOI:
- 10.48550/arXiv.1706.05473
- arXiv:
- arXiv:1706.05473
- Bibcode:
- 2017arXiv170605473H
- Keywords:
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- Mathematics - Group Theory
- E-Print:
- final preprint version, to appear in Proc. Lond. Math. Soc