## The Seiberg-Witten equations on a surface times a circle

##### Author(s)

Lopes, William Manuel
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##### Other Contributors

Massachusetts Institute of Technology. Dept. of Mathematics.

##### Advisor

Tomasz S. Mrowka.

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Show full item record##### Abstract

In this thesis I study the Seiberg-Witten equations on the product of a genus g surface [Sigma] and a circle. I exploit S1 invariance to reduce to the vortex equations on [Sigma] and thus completely describe the Seiberg-Witten monopoles. In the case where the monopoles are not Morse-Bott regular, I explicitly perturb the equations to obtain such a situation and thus find a candidate for the chain complex that calculates the Seiberg-Witten Floer homology groups.

##### Description

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010. Cataloged from PDF version of thesis. Includes bibliographical references (p. 63).

##### Date issued

2010##### Department

Massachusetts Institute of Technology. Dept. of Mathematics.##### Publisher

Massachusetts Institute of Technology

##### Keywords

Mathematics.