Moduli spaces of self-dual connections over asymptotically locally flat gravitational instantons
| dc.creator | Etesi, Gabor | |
| dc.creator | Jardim, Marcos | |
| dc.date | 2006-08-24 | |
| dc.date | 2009-05-20 | |
| dc.date.accessioned | 2026-07-07T13:16:35Z | |
| dc.date.available | 2026-07-07T13:16:35Z | |
| dc.description | We investigate Yang--Mills instanton theory over four dimensional asymptotically locally flat (ALF) geometries, including gravitational instantons of this type, by exploiting the existence of a natural smooth compactification of these spaces introduced by Hausel--Hunsicker--Mazzeo. First referring to the codimension 2 singularity removal theorem of Sibner--Sibner and Rade we prove that given a smooth, finite energy, self-dual SU(2) connection over a complete ALF space, its energy is congruent to a Chern--Simons invariant of the boundary three-manifold if the connection satisfies a certain holonomy condition at infinity and its curvature decays rapidly. Then we introduce framed moduli spaces of self-dual connections over Ricci flat ALF spaces. We prove that the moduli space of smooth, irreducible, rapidly decaying self-dual connections obeying the holonomy condition with fixed finite energy and prescribed asymptotic behaviour on a fixed bundle is a finite dimensional manifold. We calculate its dimension by a variant of the Gromov--Lawson relative index theorem. As an application, we study Yang--Mills instantons over the flat R^3 x S^1, the multi-Taub--NUT family, and the Riemannian Schwarzschild space. | |
| dc.description | 29 pages, LaTeX, no figures; Lemma 2.1 corrected | |
| dc.identifier | https://arxiv.org/abs/math/0608597 | |
| dc.identifier | http://arxiv.org/abs/math/0608597 | |
| dc.identifier | Article:Commun.Math.Phys.280:285-313 (2008); Erratum: Commun.Math.Phys.288:799-800 (2009) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230839 | |
| dc.subject | Differential Geometry | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | 53C26 (Primary); 53C29, 58J20, 58J28, 83C15 (Secondary) | |
| dc.title | Moduli spaces of self-dual connections over asymptotically locally flat gravitational instantons | |
| dc.type | text |