Tuesday, July 23, 2013 - from 17:00 to 17:25
Classifying spaces of groups are objects of great importance in topology, geometry and algebra. Their homology and cohomology were studied for a long time, since they capture information about principal bundles and fibre bundles. In this talk I will introduce a product in the homology of classifying spaces of compact Lie groups. The construction is geometric and quite simple. For finite groups this product coincides with the cup product in negative Tate cohomology. In the talk I will give some results regarding the product for connected groups, indicating the vanishing of this product for many groups, but not all.