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.
Citation
Georgios Daskalopoulos. Jonathan Weitsman. Richard A. Wentworth. Graeme Wilkin. "Morse theory and hyperkähler Kirwan surjectivity for Higgs bundles." J. Differential Geom. 87 (1) 81 - 116, January 2011. https://doi.org/10.4310/jdg/1303219773
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