Homotopy Type of Moduli Spaces of G-Higgs Bundles and Reducibility of the Nilpotent Cone

C. Florentino; P. B. Gothen; A. Nozad

doi:10.1016/j.bulsci.2018.10.002

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arXiv · 1805.10081

Homotopy Type of Moduli Spaces of G-Higgs Bundles and Reducibility of the Nilpotent Cone

C. Florentino·P. B. Gothen·A. Nozad

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Abstract

Let $G$ be a real reductive Lie group, and $H^{\mathbb{C}}$ the complexification of its maximal compact subgroup $H\subset G$. We consider classes of semistable $G$-Higgs bundles over a Riemann surface $X$ of genus $g\geq2$ whose underlying $H^{\mathbb{C}}$-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 $H^{\mathbb{C}}$-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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C. Florentino, P. B. Gothen, A. Nozad. 2018-05-25. Homotopy Type of Moduli Spaces of G-Higgs Bundles and Reducibility of the Nilpotent Cone. https://doi.org/10.1016/j.bulsci.2018.10.002

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