Morse Theory for the Space of Higgs Bundles
| dc.creator | Wilkin, Graeme | |
| dc.date | 2006-11-05 | |
| dc.date | 2008-06-06 | |
| dc.date.accessioned | 2026-07-07T09:42:53Z | |
| dc.date.available | 2026-07-07T09:42:53Z | |
| dc.description | Here we 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 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 Harder-Narasimhan-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. | |
| dc.description | 45 pages, to appear Communications in Analysis and Geometry | |
| dc.identifier | https://arxiv.org/abs/math/0611113 | |
| dc.identifier | http://arxiv.org/abs/math/0611113 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162351 | |
| dc.subject | Differential Geometry | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 58E15 | |
| dc.title | Morse Theory for the Space of Higgs Bundles | |
| dc.type | text |