Index theorems and magnetic monopoles on asymptotically conic manifolds
Name
681923895-MIT.pdf
Description
Full printable version
Size
6.19 MB
Format
Adobe PDF
Checksum (MD5)
34800d05b07101e68c80e549c5f39eb2
Author(s)
Kottke, Christopher N. (Christopher Nicholas)
Advisor(s)
Richard B. Melrose.
Date Issued
2010
Publisher
Massachusetts Institute of Technology
Abstract
In this thesis, I investigate the index of Callias type operators on asymptotically conic manifolds (also known as asymptotically locally Euclidean manifolds or scattering manifolds) and give an application to the moduli space of magnetic monopoles on these spaces. The index theorem originally due to C. Callias and later generalized by N. Anghel and others concerns operators of the form ... is a family of Hermitian invertible matrices. The first result is a pseudodifferential version of this index theorem, in the spirit of of the K-theoretic proof of the Atiyah-Singer index theorem, using the theory of scattering pseudodifferential operators. The second result is an extension to the case where [Iota] has constant rank nullspace bundle at infinity, using a b-to-scattering transition calculus of pseudodifferential operators. Finally I discuss magnetic monopoles, which are solutions to the Bogomolny equation ... principal bundle over a complete 3-manifold, and I show how the previous results can be applied to compute the dimension of the moduli space of monopoles over asymptotically conic manifolds whose boundary is homeomorphic to a disjoint union of spheres.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 101-102).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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copyright. They may be viewed from this source for any purpose, but
reproduction or distribution in any format is prohibited without written
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