Contributions to sutured monopole and sutured instanton Floer homology theories
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1191267083-MIT.pdf
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1.59 MB
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Author(s)
Li, Zhenkun,Ph. D.Massachusetts Institute of Technology.
Advisor(s)
Tomasz S. Mrowka.
Date Issued
2020
Publisher
Massachusetts Institute of Technology
Abstract
In this thesis, we present the development of some aspects of sutured monopole and sutured instanton Floer homology theories. Sutured monopole and instanton Floer homologies were introduced by Kronheimer and Mrowka. They are the adaption of monopole and instanton Floer theories to the case of balanced sutured manifolds, which are compact oriented 3-manifolds together with some special data on the boundary called the suture. We construct the gluing and cobordism maps in these theories, construct gradings associated to properly embedded surfaces inside the balanced sutured manifolds, and use these tools to further construct minus versions of knot Floer homologies in monopole and instanton theories. These constructions contribute to laying down a solid basis in sutured monopole and sutured instanton Floer homology theories, upon which we could develop further applications.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020
Cataloged from the official PDF of thesis.
Includes bibliographical references (pages 261-267).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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