Moduli Spaces of Self-Dual Connections over Asymptotically Locally Flat Gravitational Instantons

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 t...

Celý popis

Uloženo v:

Podrobná bibliografie
Vydáno v:	Communications in mathematical physics Ročník 280; číslo 2; s. 285 - 313
Hlavní autoři:	Etesi, Gábor, Jardim, Marcos
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Berlin/Heidelberg Springer-Verlag 01.06.2008 Springer
Témata:	Classical and Quantum Gravitation Complex Systems Exact sciences and technology General topology Mathematical analysis Mathematical and Computational Physics Mathematical methods in physics Mathematical Physics Mathematics Ordinary differential equations Other topics in mathematical methods in physics Physics Physics and Astronomy Quantum Physics Relativity Theory Sciences and techniques of general use Several complex variables and analytic spaces Theoretical Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds Modulus Space Global Gauge Gravitational Instantons Vector Bundle Holonomy Condition Geometry Mathematical manifolds Gromov theorem Three manifold Energy space Asymptotic behavior Curvature Mathematical physics
ISSN:	0010-3616, 1432-0916
On-line přístup:	Získat plný text
Tagy:	Přidat tag Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!

Popis
Shrnutí:	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 Råde 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 , the multi-Taub–NUT family, and the Riemannian Schwarzschild space.
ISSN:	0010-3616 1432-0916
DOI:	10.1007/s00220-008-0466-9