Contributions to sutured monopole and sutured instanton Floer homology theories
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2020
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| Online Access: | https://hdl.handle.net/1721.1/126928 |
| _version_ | 1826195367371210752 |
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| author | Li, Zhenkun,Ph. D.Massachusetts Institute of Technology. |
| author2 | Tomasz S. Mrowka. |
| author_facet | Tomasz S. Mrowka. Li, Zhenkun,Ph. D.Massachusetts Institute of Technology. |
| author_sort | Li, Zhenkun,Ph. D.Massachusetts Institute of Technology. |
| collection | MIT |
| description | Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020 |
| first_indexed | 2024-09-23T10:11:34Z |
| format | Thesis |
| id | mit-1721.1/126928 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T10:11:34Z |
| publishDate | 2020 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1269282020-09-04T03:35:12Z Contributions to sutured monopole and sutured instanton Floer homology theories Li, Zhenkun,Ph. D.Massachusetts Institute of Technology. Tomasz S. Mrowka. Massachusetts Institute of Technology. Department of Mathematics. Massachusetts Institute of Technology. Department of Mathematics Mathematics. 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 2020-09-03T16:41:10Z 2020-09-03T16:41:10Z 2020 2020 Thesis https://hdl.handle.net/1721.1/126928 1191267083 eng 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 267 pages application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Li, Zhenkun,Ph. D.Massachusetts Institute of Technology. Contributions to sutured monopole and sutured instanton Floer homology theories |
| title | Contributions to sutured monopole and sutured instanton Floer homology theories |
| title_full | Contributions to sutured monopole and sutured instanton Floer homology theories |
| title_fullStr | Contributions to sutured monopole and sutured instanton Floer homology theories |
| title_full_unstemmed | Contributions to sutured monopole and sutured instanton Floer homology theories |
| title_short | Contributions to sutured monopole and sutured instanton Floer homology theories |
| title_sort | contributions to sutured monopole and sutured instanton floer homology theories |
| topic | Mathematics. |
| url | https://hdl.handle.net/1721.1/126928 |
| work_keys_str_mv | AT lizhenkunphdmassachusettsinstituteoftechnology contributionstosuturedmonopoleandsuturedinstantonfloerhomologytheories |