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Paper   IPM / M / 16068
School of Mathematics
  Title:   Homotopy type of moduli spaces of G-Higgs bundles and reducibility of the nilpotent cone
  Author(s):  azizeh Nozad (Joint with P. B. Gothen and C. Florentino)
  Status:   Published
  Journal: Bull. Sci. Math.
  Vol.:  150
  Year:  2019
  Pages:   88-101
  Supported by:  IPM
et G be a real reductive Lie group, and H\mathbbC the complexification of its maximal compact subgroup HG. We consider classes of semistable G-Higgs bundles over a Riemann surface X of genus g ≥ 2 whose underlying H\mathbbC-principal bundle is unstable. This allows us to find obstructions to a deformation retract from the moduli space of G-Higgs bundles over X to the moduli space of H\mathbbC-bundles over X, in contrast with the situation when g=1, and to show reducibility of the nilpotent cone of the moduli space of G-Higgs bundles, for G complex.

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