ActionDimension of Groups
ActionDimension of Groups

William Browder, Princeton University
Fine Hall 214
Please note change of time and location. This is a joint Topology/Algebraic Topology seminar. For a group G, we define a notion of dimension in terms of dimension change of the of the top homology between a free G space X and it's quotient X/G. We show that this is well defined and calculate this "Actiondimension" for certain groups, including finitely generated solvable groups, free groups, finite groups, and connected Lie groups. As a consequence we give a positive answer to a conjecture of J Kollar: Let f: R^n > T^n be the universal covering and M a closed submanifold in T^n = (S^1)^n such that f^{1}(M) has the homotopy type of a finite complex, then M = T^n.