Negative curvature in locally reducible Artin groups

Jill Mastrocola

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arXiv · 2405.00173

Negative curvature in locally reducible Artin groups

Jill Mastrocola

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Abstract

In this paper, we define the 2-complete Artin complex and show that it is systolic for locally reducible Artin groups. The stabilizers of simplices in this complex are exactly the proper parabolic subgroups which are "2-complete." We use this systolicity to show that parabolic subgroups, with 2-completions that are not the whole Artin group, are weakly malnormal. This allows us to conclude that many locally reducible Artin groups are acylindrically hyperbolic.

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Jill Mastrocola. 2024-04-30. Negative curvature in locally reducible Artin groups. https://arxiv.org/abs/2405.00173

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