Abstract (EN):
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 Poincare polynomials of these spaces for some low rank groups G, such as Sp(4, IR) and U(2, 2). We also compare these real moduli spaces to the real points of the corresponding complex moduli spaces, and describe the geometry of many examples.
Idioma:
Inglês
Tipo (Avaliação Docente):
Científica
Nº de páginas:
20