代数研讨班：The K(pi,1)-conjecture for Artin groups via combinatorial non-positive curvature

中科院数学与系统科学研究院

数学研究所

学术报告

代数研讨班

报告人：黄靖尹 副教授 (The Ohio State University)

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

时  间：2024.6.26（星期三）16：00-17：00

地  点：N913

摘  要：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.