2026-09-20T07:02:12Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1269282026-06-16T18:54:31Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Tomasz S. Mrowka.
Li, Zhenkun,Ph. D.Massachusetts Institute of Technology.
Massachusetts Institute of Technology. Department of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2020-09-03T16:41:10Z
2020-09-03T16:41:10Z
2020
2020
https://hdl.handle.net/1721.1/126928
1191267083
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).
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.
by Zhenkun Li.
Ph.D.
Ph.D. Massachusetts Institute of Technology, Department of Mathematics
267 pages
eng
Massachusetts Institute of Technology
MIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided.
http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Contributions to sutured monopole and sutured instanton Floer homology theories
Thesis
application/pdf
2020-09-03T16:41:10Z
Publication
Doctoral
Math
unknown
unknown
<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="3e498e61-4278-4fe9-a4ab-12b5f8ad37d3">
<Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type>
<Language>eng</Language>
<Title>Contributions to sutured monopole and sutured instanton Floer homology theories</Title>
<PublishedIn>
<Publication>
</Publication>
</PublishedIn>
<PublicationDate>2020</PublicationDate>
<Authors>
<Author>
<DisplayName>Li, Zhenkun,Ph. D.Massachusetts Institute of Technology.</DisplayName>
<Affiliation>
<OrgUnit>
</OrgUnit>
</Affiliation>
</Author>
</Authors>
<Editors>
</Editors>
<Publishers>
<Publisher>
<DisplayName>Massachusetts Institute of Technology</DisplayName>
<OrgUnit />
</Publisher>
</Publishers>
<License>http://dspace.mit.edu/handle/1721.1/7582</License>
<Keyword>Mathematics.</Keyword>
<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.</Abstract>
<Access xmlns="http://purl.org/coar/access_right"
>
</Access>
</Publication>