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Paper IPM / M / 16068  


Abstract:  
et G be a real reductive Lie group, and H^{\mathbbC} the complexification of its maximal compact subgroup H ⊂ G. We consider classes of semistable GHiggs 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 GHiggs 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 GHiggs bundles, for G complex.
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