Title:
Legendrian and transverse knots and their invariants

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dc.contributor.advisor Etnyre, John B.
dc.contributor.author Tosun, Bulent en_US
dc.contributor.committeeMember Dan Margalit
dc.contributor.committeeMember Igor Belegradek
dc.contributor.committeeMember Mohammad Ghomi
dc.contributor.committeeMember Will H. Kazez
dc.contributor.department Mathematics en_US
dc.date.accessioned 2012-09-20T18:22:22Z
dc.date.available 2012-09-20T18:22:22Z
dc.date.issued 2012-08-14 en_US
dc.description.abstract In 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.description.degree PhD en_US
dc.identifier.uri http://hdl.handle.net/1853/44880
dc.publisher Georgia Institute of Technology en_US
dc.subject Knots in contact geometry. cabling en_US
dc.subject.lcsh Knot theory
dc.subject.lcsh Contact manifolds
dc.title Legendrian and transverse knots and their invariants en_US
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.advisor Etnyre, John B.
local.contributor.corporatename College of Sciences
local.contributor.corporatename School of Mathematics
relation.isAdvisorOfPublication a9264768-2f0a-4f64-842d-cff98031262b
relation.isOrgUnitOfPublication 85042be6-2d68-4e07-b384-e1f908fae48a
relation.isOrgUnitOfPublication 84e5d930-8c17-4e24-96cc-63f5ab63da69
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