Morse Theory for the Space of Higgs Bundles
نویسنده
چکیده
Here we prove the necessary analytic results to construct a Morse theory for the YangMills-Higgs functional on the space of Higgs bundles over a compact Riemann surface. The main result is that the gradient flow with initial conditions (A, φ) converges to a critical point of this functional, the isomorphism class of which is given by the graded object associated to the HarderNarasimhan-Seshadri filtration of (A, φ). In particular, the results of this paper show that the failure of hyperkähler Kirwan surjectivity for rank 2 fixed determinant Higgs bundles does not occur because of a failure of the existence of a Morse theory.
منابع مشابه
Morse Theory and Hyperkähler Kirwan Surjectivity for Higgs Bundles
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. CONTENTS
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