Dirac operators and monopoles with singularities

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2007

Author dc:creator

• Yang, Fangyun, Ph. D. Massachusetts Institute of Technology

Advisor dc:contributor.advisor

• Tomasz Mrowka.

• Mathematics.

Statement dc:rights

• 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/41723

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/41723