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Moduli spaces of self-dual connections over asymptotically locally flat gravitational instantons
| Content Provider | Semantic Scholar |
|---|---|
| Author | Etesi, Gabor |
| Copyright Year | 2009 |
| Abstract | 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 R̊ade 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 threemanifold 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 selfdual 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 R3 × S1, the multiTaub–NUT family, and the Riemannian Schwarzschild space. AMS Classification: Primary: 53C26; Secondary: 53C29, 58J20, 58J28, 83C15 ∗etesi@math.bme.hu and etesi@ime.unicamp.br †jardim@ime.unicamp.br G.Etesi, M. Jardim: Yang–Mills instantons on ALF gravitational instantons 2 |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0608597v7.pdf |
| Alternate Webpage(s) | http://math.bme.hu/~etesi/alf2.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0608597v5.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0608597v6.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0608597v2.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0608597v3.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0608597v1.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Byers-Yang theorem Dual Flatfoot Irreducibility Ising model Keneth Alden Simons Neoplasm Metastasis Tree nut YANG manifold |
| Content Type | Text |
| Resource Type | Article |
