# Action dimension and L^2 Cohomology

NPCW05 - Group actions and cohomology in non-positive curvature

Co-authors: Michael Davis (Ohio State University), Giang Le ()

The action dimension of a group G is the minimal dimension of contractible manifold that G acts on properly discontinuously. Conjecturally, if a group has nontrivial cohomology in dimension n, the action dimension of G is bounded below by 2n. I will describe examples where this conjecture holds, including lattices in Euclidean buildings, graph products, and fundamental groups of some complex hyperplane complements. This will involve joint work with Mike Davis and Giang Le, as well as Grigori Avramidi, Mike Davis, and Boris Okun.

This talk is part of the Isaac Newton Institute Seminar Series series.