2026-09-19T23:27:20Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/417232022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Tomasz Mrowka.
Yang, Fangyun, Ph. D. Massachusetts Institute of Technology
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2008-05-19T16:12:15Z
2008-05-19T16:12:15Z
2007
2007
http://hdl.handle.net/1721.1/41723
225060752
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2007.
Includes bibliographical references (p. 75-77).
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.
by Fangyun Yang.
Ph.D.
77 p.
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Dirac operators and monopoles with singularities
Thesis
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