On spaces of homomorphisms and spaces of representations

Fred Cohen, University of Rochester and IAS
Fine Hall 314

The subject of this talk is the structure of the space of homomorphisms from a group $\pi$ to a Lie group $G$ denoted $Hom(\pi,G)$. The space of representations $Hom(\pi,G)/G$ obtained from the adjoint action of $G$ will be considered. In special cases, these spaces can be assembled into a single space analogous to the classifying space of the group $G$. Properties of these spaces will be developed. This talk is based on joint work with A. Adem, E. Torres, and J. Gomez.