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K(π, 1)-conjecture for Artin groups via combinatorial non-positive curvature

Hot Topics: Artin Groups and Arrangements - Topology, Geometry, and Combinatorics March 11, 2024 - March 15, 2024

March 14, 2024 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Jingyin Huang (Ohio State University)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Tags/Keywords

  • Artin groups

  • braid groups

  • Coxeter groups

  • reflection groups

  • Garside structures

  • classifying spaces

  • hyperplane arrangements

  • subspace arrangements

  • configuration spaces

  • geometric group theory

  • Matroids

  • cohomology

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

K(π, 1)-conjecture for Artin groups via combinatorial non-positive curvature
Abstract

We establish a close connection between simple properties about 4-cycles in certain graphs and the K(pi,1)-conjecture, via elements of non-positively curvature geometry. We also propose a new approach for studying this conjecture. As a consequence, we deduce many new cases of Artin groups which satisfies the K(pi,1)-conjecture. If time allows, I will also discuss a connections between K(pi,1)-conjecture for Artin groups and finding certain types of sub-arrangements inside the deconing of arrangements associated with finite Coxeter groups.
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Video/Audio Files

K(π, 1)-conjecture for Artin groups via combinatorial non-positive curvature

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