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Showing 1 to 7 of 7 for “"contact topology"”.
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Legendrian Torus Links
<p>A basic problem in contact topology is to determine whether two Legendrian knots or links are equivalent. In this dissertation, we will study the equivalence and non-equivalence of Legendrian links that are topologically torus links.</p>
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A Tourist's Account of Characteristic Foliations on Convex Surfaces in 3-D Contact Geometry
… begin with a rapid introduction to the theory of contact topology, first spending more time than you would probably want on developing the notion of contact manifold before launching right into the thick of the theory. The tools of characteristic foliations and convex surfaces are introduced next, …
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Bordered Legendrian knots and sutured Legendrian invariants
… 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.
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Bordered Sutured Floer Homology
… one defined by Honda, Kazez, and Matic, using contact topology and open book decompositions).
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Exact Lagrangian Fillings of Legendrian links and Weinstein 4-manifolds
… approach to studying symplectic manifolds with contact boundary is to consider Lagrangian submanifolds with Legendrian boundary; in particular one can study exact Lagrangian fillings of Legendrian links. There are still many open questions on the spaces of exact Lagrangian fillings of Legendrian …
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Connections between Floer-type invariants and Morse-type invariants of Legendrian knots.
We investigate existing Legendrian knot invariants and discover new connections between the theory of generating families, normal rulings and the Chekanov-Eliashberg differential graded algebra: CE-DGA). Given a Legendrian knot $\sK$ with generic front projection $\sfront$, we define a …
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Embedded contact knot homology and a surgery formula
Embedded contact homology is an invariant of closed oriented contact 3-manifolds first defined by Hutchings, and is isomorphic to both Heegard Floer homology (by the work of Colin, Ghiggini and Honda) and Seiberg-Witten Floer cohomology (by the work of Taubes). The embedded contact chain complex is …