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Metric systolicity and two-dimensional Artin groups

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Huang,  Jingyin
Max Planck Institute for Mathematics, Max Planck Society;

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Citation

Huang, J., & Osajda, D. (2019). Metric systolicity and two-dimensional Artin groups. Mathematische Annalen, 374(3-4), 1311-1352. doi:10.1007/s00208-019-01823-6.


Cite as: http://hdl.handle.net/21.11116/0000-0004-68DD-F
Abstract
We introduce the notion of metrically systolic simplicial complexes. We study geometric and large-scale properties of such complexes and of groups acting on them geometrically. We show that all two-dimensional Artin groups act geometrically on metrically systolic complexes. As direct corollaries we obtain new results on two-dimensional Artin groups and all their finitely presented subgroups: we prove that the Conjugacy Problem is solvable, and that the Dehn function is quadratic. We also show several large-scale features of finitely presented subgroups of two-dimensional Artin groups, lying background for further studies concerning their quasi-isometric rigidity.