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Morse theory and hyperkahler kirwan surjectivity for higgs bundles

Georgios Daskalopoulos Brown University Jonathan Weitsman Northeastern University Richard A.Wentworth University of Maryland Graeme Wilkin University of Colorado

Differential Geometry mathscidoc:1609.10206

Journal of Differential Geometry, 87, (1), 81-115, 2011
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 hyperk¨ahler Kirwan map is surjective for the non-fixed determinant case.
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@inproceedings{georgios2011morse,
  title={MORSE THEORY AND HYPERKAHLER KIRWAN SURJECTIVITY FOR HIGGS BUNDLES},
  author={Georgios Daskalopoulos, Jonathan Weitsman, Richard A.Wentworth, and Graeme Wilkin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911230803196931863},
  booktitle={Journal of Differential Geometry},
  volume={87},
  number={1},
  pages={81-115},
  year={2011},
}
Georgios Daskalopoulos, Jonathan Weitsman, Richard A.Wentworth, and Graeme Wilkin. MORSE THEORY AND HYPERKAHLER KIRWAN SURJECTIVITY FOR HIGGS BUNDLES. 2011. Vol. 87. In Journal of Differential Geometry. pp.81-115. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911230803196931863.
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