Morse theory and hyperkähler Kirwan surjectivity for Higgs bundles

TY - JOUR

T1 - Morse theory and hyperkähler Kirwan surjectivity for Higgs bundles

AU - Daskalopoulos, Georgios

AU - Weitsman, Jonathan

AU - Wentworth, Richard

AU - Wilkin, Graeme Peter Desmond

PY - 2011/1/1

Y1 - 2011/1/1

N2 - 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.

AB - 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.

U2 - 10.4310/jdg/1303219773

DO - 10.4310/jdg/1303219773

M3 - Article

SN - 0022-040X

VL - 87

SP - 81

EP - 116

JO - Journal of Differential Geometry

JF - Journal of Differential Geometry

IS - 1

ER -