Abstract: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-posi...
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