Abstract：A hyperplane arrangement in C^n is the manifold obtained by removing a collection of affine complex dimension one hyperplanes from C^n. Despite the simplicity of the definition and the long history of studying them, even basic questions on their fundamental groups still remain open. One important scenario of studying, is that the collection of hyperplanes has extra symmetry - namely t...
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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