Research output: Contribution to journal › Article

**Morse theory for the space of Higgs bundles.** / Wilkin, Graeme Peter Desmond.

Research output: Contribution to journal › Article

Wilkin, GPD 2008, 'Morse theory for the space of Higgs bundles', *Communications in Analysis and Geometry*, vol. 16, no. 2, pp. 283-332.

Wilkin, G. P. D. (2008). Morse theory for the space of Higgs bundles. *Communications in Analysis and Geometry*, *16*(2), 283-332.

Wilkin GPD. Morse theory for the space of Higgs bundles. Communications in Analysis and Geometry. 2008 Jan 1;16(2):283-332.

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title = "Morse theory for the space of Higgs bundles",

abstract = "The purpose of this paper is to prove the necessary analytic results to construct a Morse theory for the Yang–Mills–Higgs functional on the space of Higgs bundles over a compact Riemann surface.The main result is that the gradient flow converges to a critical point of this functional, the isomorphism class of which is given by the graded object associated to theHarder–Narasimhan–Seshadri filtration of the initial condition. In particular,the results of this paper show that the failure of hyperkahler Kirwan surjectivity for rank 2 fixed determinant Higgs bundles does not occur because of a failure of the existence of a Morse theory.",

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AB - The purpose of this paper is to prove the necessary analytic results to construct a Morse theory for the Yang–Mills–Higgs functional on the space of Higgs bundles over a compact Riemann surface.The main result is that the gradient flow converges to a critical point of this functional, the isomorphism class of which is given by the graded object associated to theHarder–Narasimhan–Seshadri filtration of the initial condition. In particular,the results of this paper show that the failure of hyperkahler Kirwan surjectivity for rank 2 fixed determinant Higgs bundles does not occur because of a failure of the existence of a Morse theory.

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