Morse theory and hyperkähler Kirwan surjectivity for Higgs bundles
Daskalopoulos, Georgios ; Weitsman, Jonathan ; Wentworth, Richard A. ; Wilkin, Graeme
J. Differential Geom., Tome 87 (2011) no. 1, p. 81-116 / Harvested from Project Euclid
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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.
Publié le : 2011-01-15
Classification:  
@article{1303219773,
     author = {Daskalopoulos, Georgios and Weitsman, Jonathan and Wentworth, Richard A. and Wilkin, Graeme},
     title = {Morse theory and hyperk\"ahler Kirwan surjectivity for Higgs bundles},
     journal = {J. Differential Geom.},
     volume = {87},
     number = {1},
     year = {2011},
     pages = { 81-116},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1303219773}
}

Daskalopoulos, Georgios; Weitsman, Jonathan; Wentworth, Richard A.; Wilkin, Graeme. Morse theory and hyperkähler Kirwan surjectivity for Higgs bundles. J. Differential Geom., Tome 87 (2011) no. 1, pp.  81-116. http://gdmltest.u-ga.fr/item/1303219773/