Abstract:

Abstract: The main direction of this topic is the structure for the space of homomorphisms from a free abelian group to a Lie group as well as associated quotients spaces obtained from the adjoint representation, the associated space of representations. These spaces admit the additional structure of a simplicial space at the heart of work of Jardine. What is the fundamental group or the first homology group of the associated space ? This deceptively elementary question as well as more global information is the subject of this talk based on joint work with A. Adem, E. Torres, and J. Gomez.