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


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 A. Wentworth. Graeme Wilkin. "Morse theory and hyperkähler Kirwan surjectivity for Higgs bundles." J. Differential Geom. 87 (1) 81 - 116, January 2011.


Published: January 2011
First available in Project Euclid: 19 April 2011

zbMATH: 1230.14046
MathSciNet: MR2786591
Digital Object Identifier: 10.4310/jdg/1303219773

Rights: Copyright © 2011 Lehigh University

Vol.87 • No. 1 • January 2011
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