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The Seiberg-Witten equations on 3-manifolds with boundary

Citation

Yang, Qing (1999) The Seiberg-Witten equations on 3-manifolds with boundary. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:12152011-111123232

Abstract

The Seiberg-Witten equations have proved to be quite powerful in studying smooth 4-manifolds since their landing in 1994. The corresponding Seiberg-Witten theory on closed 3-manifolds can either be obtained by a dimension reduction from the four-dimensional theory, or by following Floer's approach. Here we investigate the theory on 3-manifolds with boundary. The solutions to the Seiberg-Witten equations are identified with critical points to the Chern-Simons-Dirac functional, regarded as a section of the U(1) bundle over the quotient B of the configuration space. An infinite tube [0, ∞) X ∑ is added to the compact manifold and the asymptotic behavior of the solutions on the cylindrical end are studied. The moduli spaces of solutions under gauge group action are finite dimensional, compact and generically smooth. For a generic perturbation h, the moduli space M_h can be related to the moduli space M_L of the Kähler-Vortex equations on the boundary surface ∑, via a limit ing map r, which is a LagTangian immersion with respect to a canonical symplectic structure on M_L. Moreover, for a family of admissible perturbations, the moduli spaces for the perturbed Seiberg-Witten equations are mutually Legendrian cobordant.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Mrowka, Tomasz
Thesis Committee:
  • Unknown, Unknown
Defense Date:8 March 1999
Record Number:CaltechTHESIS:12152011-111123232
Persistent URL:http://resolver.caltech.edu/CaltechTHESIS:12152011-111123232
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6751
Collection:CaltechTHESIS
Deposited By: John Wade
Deposited On:15 Dec 2011 19:32
Last Modified:01 Aug 2014 17:11

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