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dc.contributor.advisorTomasz S. Mrowka.en_US
dc.contributor.authorLi, Zhenkun,Ph. D.Massachusetts Institute of Technology.en_US
dc.contributor.otherMassachusetts Institute of Technology. Department of Mathematics.en_US
dc.date.accessioned2020-09-03T16:41:10Z
dc.date.available2020-09-03T16:41:10Z
dc.date.copyright2020en_US
dc.date.issued2020en_US
dc.identifier.urihttps://hdl.handle.net/1721.1/126928
dc.descriptionThesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020en_US
dc.descriptionCataloged from the official PDF of thesis.en_US
dc.descriptionIncludes bibliographical references (pages 261-267).en_US
dc.description.abstractIn 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.en_US
dc.description.statementofresponsibilityby Zhenkun Li.en_US
dc.format.extent267 pagesen_US
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsMIT 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.en_US
dc.rights.urihttp://dspace.mit.edu/handle/1721.1/7582en_US
dc.subjectMathematics.en_US
dc.titleContributions to sutured monopole and sutured instanton Floer homology theoriesen_US
dc.typeThesisen_US
dc.description.degreePh. D.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.identifier.oclc1191267083en_US
dc.description.collectionPh.D. Massachusetts Institute of Technology, Department of Mathematicsen_US
dspace.imported2020-09-03T16:41:10Zen_US
mit.thesis.degreeDoctoralen_US
mit.thesis.departmentMathen_US


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