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...
AbstractThe classical Hodge conjecture states that for a smooth projective variety any rational (p,p)-class can be represented by an algebraic cycle. The first non-trivial case for abelian varietie