Morse Theory and Hyperkahler Kirwan Surjectivity for Higgs Bundles
Symplectic Geometry
2009-10-23 v2 Differential Geometry
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 hyperk\"ahler Kirwan map is surjective for the non-fixed determinant case.
Keywords
Cite
@article{arxiv.math/0701560,
title = {Morse Theory and Hyperkahler Kirwan Surjectivity for Higgs Bundles},
author = {Georgios Daskalopoulos and Jonathan Weitsman and Richard Wentworth and Graeme Wilkin},
journal= {arXiv preprint arXiv:math/0701560},
year = {2009}
}
Comments
33 pages. Corrected Betti number formulae, added a description of the \Gamma_2-invariant cohomology in the fixed determinant case (correcting an earlier error), explained the Morse-Bott isomorphism (Proposition 3.1) in detail