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dc.contributor.advisorTomasz Mrowka.en_US
dc.contributor.authorSivek, Steven (Steven W.)en_US
dc.contributor.otherMassachusetts Institute of Technology. Dept. of Mathematics.en_US
dc.date.accessioned2011-12-19T19:00:59Z
dc.date.available2011-12-19T19:00:59Z
dc.date.copyright2011en_US
dc.date.issued2011en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/67814
dc.descriptionThesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.en_US
dc.descriptionCataloged from PDF version of thesis.en_US
dc.descriptionIncludes bibliographical references (p. 115-120).en_US
dc.description.abstractIn this thesis we apply techniques from the bordered and sutured variants of Floer homology to study Legendrian knots. First, given a front diagram for a Legendrian knot K in S₃ which has been split into several pieces, we associate a differential graded algebra to each "bordered" piece and prove a van Kampen theorem which recovers the Chekanov-Eliashberg invariant Ch(K) of the knot from the bordered DGAs. This leads to the construction of morphisms Ch(K) --> Ch(K') corresponding to certain Legendrian tangle replacements and many related applications. We also examine several examples in detail, including Legendrian Whitehead doubles and the first known knot with maximal Thurston-Bennequin invariant for which Ch(K) vanishes. Second, we use monopole Floer homology for sutured manifolds to construct new invariants of Legendrian knots. These invariants reside in monopole knot homology and closely resemble Heegaard Floer invariants due to Lisca-Ozsváth-Stipsicz-Szabó, but their construction directly involves the contact topology of the knot complement and so many of their properties are easier to prove in this context. In particular, we show that these new invariants are functorial under Lagrangian concordance.en_US
dc.description.statementofresponsibilityby Steven Sivek.en_US
dc.format.extent120 p.en_US
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsM.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.en_US
dc.rights.urihttp://dspace.mit.edu/handle/1721.1/7582en_US
dc.subjectMathematics.en_US
dc.titleBordered Legendrian knots and sutured Legendrian invariantsen_US
dc.typeThesisen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Dept. of Mathematics.en_US
dc.identifier.oclc767996443en_US


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