Homotopy groups of moduli spaces of representations
  We calculate certain homotopy groups of the moduli spaces for representations of a compact oriented surface in the Lie groups GL(n,C) and U(p,q). Our approach relies on the interpretation of these representations in terms of Higgs bundles and uses Bott--Morse theory on the corresponding moduli spaces. 
Steven B. Bradlow (University of Illinois), Oscar Garcia-Prada (CSIC,   Madrid), Peter B. Gothen (Universidade do Porto)