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Morse Theory and Hyperkahler Kirwan Surjectivity for Higgs Bundles

Georgios Daskalopoulos·Jonathan Weitsman·Richard Wentworth·Graeme Wilkin
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Abstract

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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Georgios Daskalopoulos, Jonathan Weitsman, Richard Wentworth, Graeme Wilkin. 2009-10-23. Morse Theory and Hyperkahler Kirwan Surjectivity for Higgs Bundles. https://arxiv.org/abs/math/0701560

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