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dc.contributor.authorTosun, Bulenten_US
dc.date.accessioned2012-09-20T18:22:22Z
dc.date.available2012-09-20T18:22:22Z
dc.date.issued2012-08-14en_US
dc.identifier.urihttp://hdl.handle.net/1853/44880
dc.description.abstractIn this thesis, we study Legendrian and transverse isotopy problem for cabled knot types. We give two structural theorems to describe when the (r,s)- cable of a Legendrian simple knot type K is also Legendrian simple. We then study the same problem for cables of the positive trefoil knot. We give a complete classification of Legendrian and transverse cables of the positive trefoil. Our results exhibit many new phenomena in the structural understanding of Legendrian and transverse knots. we then extend these results to the other positive torus knots. The key ingredient in these results is to find necessary and sufficient conditions on maximally thickened contact neighborhoods of the positive torus knots in three sphere.en_US
dc.publisherGeorgia Institute of Technologyen_US
dc.subjectKnots in contact geometry. cablingen_US
dc.subject.lcshKnot theory
dc.subject.lcshContact manifolds
dc.titleLegendrian and transverse knots and their invariantsen_US
dc.typeDissertationen_US
dc.description.degreePhDen_US
dc.contributor.departmentMathematicsen_US
dc.description.advisorCommittee Chair: John B. Etnyre; Committee Member: Dan Margalit; Committee Member: Igor Belegradek; Committee Member: Mohammad Ghomi; Committee Member: Will H. Kazezen_US


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