Topological components of spaces of representations
نویسنده
چکیده
Since rt is a finitely generated group, the space Hom0r, G) is a real analytic variety whenever G is a connected Lie group, and is a real affine algebraic variety whenever G is a linear algebraic group over R [3, 18, 27, 32]. The group G acts on Hom(Tr, G) by conjugation and the orbit space will be denoted by Horn(n, G)/G. Geometrically, the G-orbits on Hom(Tr, G) parametrize equivalence classes of fiat principal G-bundles over S and the space Hom(n, G)/G is the deformation space of flat G-bundles over S. The characteristic classes of G-bundles determine invariants of representations n ~ G. When :r is the fundamental group of a closed surface and G is a connected Lie group, the only invariants lie in the cohomology group H2(S; lq(G))~ n~(G) (using the orientation on S). There is an obstruction map
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