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Morse theory and hyperkähler Kirwan surjectivity for Higgs bundles

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JournalJournal of Differential Geometry
DatePublished - 1 Jan 2011
Issue number1
Number of pages36
Pages (from-to)81-116
Original languageEnglish


This paper uses Morse-theoretic techniques to compute the equivariant Betti numbers of the space of semistable rank two degree zero Higgs bundles over a compact Riemann surface, a method in the spirit of Atiyah and Bott’s original approach for semistable holomorphic bundles. This leads to a natural proof that the hyperkähler Kirwan map is surjective for the non-fixed determinant case.

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