Morse Theory and Hyperkahler Kirwan Surjectivity for Higgs Bundles

Details Morse Theory and Hyperkahler Kirwan Surjectivity for Higgs Bundles Morse Theory and Hyperkahler Kirwan Surjectivity for Higgs Bundles

2007-01-19

arxiv.org/abs/math/0701560v2

Mathematics

Symplectic Geometry

33 pages. Corrected Betti number formulae, added a description of the \Gamma_2-invariant cohomology in the fixed determinant c

Scientific paper

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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