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Topology of moduli spaces of free group representations in real reductive groups
2016
Forum mathematicum
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Let G be a real reductive algebraic group with maximal compact subgroup K, and let F_r be a rank r free group. We show that the space of closed orbits in Hom(F_r,G)/G admits a strong deformation retraction to the orbit space Hom(F_r,K)/K. In particular, all such spaces have the same homotopy type. We compute the Poincaré polynomials of these spaces for some low rank groups G, such as Sp(4,R) and U(2,2). We also compare these real moduli spaces to the real points of the corresponding complex
doi:10.1515/forum-2014-0049
fatcat:tydcdh225feh5dsvst6syaq2li