Index theorems and magnetic monopoles on asymptotically conic manifolds
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.
| मुख्य लेखक: | |
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| अन्य लेखक: | |
| स्वरूप: | थीसिस |
| भाषा: | eng |
| प्रकाशित: |
Massachusetts Institute of Technology
2010
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| विषय: | |
| ऑनलाइन पहुंच: | http://hdl.handle.net/1721.1/60193 |
| _version_ | 1826215570232573952 |
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| author | Kottke, Christopher N. (Christopher Nicholas) |
| author2 | Richard B. Melrose. |
| author_facet | Richard B. Melrose. Kottke, Christopher N. (Christopher Nicholas) |
| author_sort | Kottke, Christopher N. (Christopher Nicholas) |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010. |
| first_indexed | 2024-09-23T16:35:39Z |
| format | Thesis |
| id | mit-1721.1/60193 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T16:35:39Z |
| publishDate | 2010 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/601932019-04-12T11:37:37Z Index theorems and magnetic monopoles on asymptotically conic manifolds Kottke, Christopher N. (Christopher Nicholas) Richard B. Melrose. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Dept. of Mathematics. Mathematics. Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010. Cataloged from PDF version of thesis. Includes bibliographical references (p. 101-102). 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. by Christopher N. Kottke. Ph.D. 2010-12-06T17:36:14Z 2010-12-06T17:36:14Z 2010 2010 Thesis http://hdl.handle.net/1721.1/60193 681923895 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 102 p. application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Kottke, Christopher N. (Christopher Nicholas) Index theorems and magnetic monopoles on asymptotically conic manifolds |
| title | Index theorems and magnetic monopoles on asymptotically conic manifolds |
| title_full | Index theorems and magnetic monopoles on asymptotically conic manifolds |
| title_fullStr | Index theorems and magnetic monopoles on asymptotically conic manifolds |
| title_full_unstemmed | Index theorems and magnetic monopoles on asymptotically conic manifolds |
| title_short | Index theorems and magnetic monopoles on asymptotically conic manifolds |
| title_sort | index theorems and magnetic monopoles on asymptotically conic manifolds |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/60193 |
| work_keys_str_mv | AT kottkechristophernchristophernicholas indextheoremsandmagneticmonopolesonasymptoticallyconicmanifolds |