Dirac operators and monopoles with singularities
Name
225060752-MIT.pdf
Description
Full printable version
Size
2.97 MB
Format
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Checksum (MD5)
8e7b768a443c1319b9759c5db8e4221d
Author(s)
Yang, Fangyun, Ph. D. Massachusetts Institute of Technology
Advisor(s)
Tomasz Mrowka.
Date Issued
2007
Publisher
Massachusetts Institute of Technology
Abstract
This thesis consists of two parts. In the first part of the thesis, we prove an index theorem for Dirac operators of conic singularities with codimension 2. One immediate corollary is the generalized Rohklin congruence formula. The eta function for a twisted spin Dirac operator on a circle bundle over a even dimensional spin manifold is also derived along the way. In the second part, we study the moduli space of monopoles with singularities along an embedded surface. We prove that when the base manifold is Kahler, there is a holomorphic description of the singular monopoles. The compactness for this case is also proved.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2007.
Includes bibliographical references (p. 75-77).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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