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Topology/Geometry Seminar

The \(K(\pi,1)\)-conjecture for Artin groups via combinatorial non-positive curvature

Jingyin Huang (Ohio State University)

Location:  Hill 705
Date & time: Tuesday, 16 April 2024 at 4:00PM - 5:00PM

The \(K(\pi,1)\)-conjecture for reflection arrangement complements, due to Arnold, Brieskorn, Pham, and Thom, predicts that certain complexified hyperplane complements associated to infinite reflection groups are Eilenberg MacLane spaces. We establish a close connection between a very simple property in metric graph theory about 4-cycles and the \(K(\pi,1)\)-conjecture, via elements of non-positively curvature geometry. We also propose a new approach for studying the \(K(\pi,1)\)-conjecture. As a consequence, we deduce a large number of new cases of Artin groups which satisfies the \(K(\pi,1)\)-conjecture.