The fundamental group of $\text{ Hom}(\bb Z^k,G)$

The fundamental group of $\text{ Hom}(\bb Z^k,G)$

Mon, 08/11/2010
15:45 		Alexandra Pettet (Oxford) Topology Seminar Add to calendar
The fundamental group of $ \text{ Hom}(\bb Z^k,G) $
Let $ G $ be a compact Lie group, and consider the variety $ \text {Hom} (\bb Z^k,G) $ of representations of the rank $ k $ abelian free group $ \bb Z^k $ into $ G $. We prove that the fundamental group of $ \text {Hom} (\bb Z^k,G) $ is naturally isomorphic to direct product of $ k $ copies of the fundamental group of $ G $. This is joint work with Jose Manuel Gomez and Juan Souto.