Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 19 of 19 for “"Legendrian"”.
-
Bordered Legendrian knots and sutured Legendrian invariants
… 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 …
-
Legendrian Torus Links
… 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>
-
Invariants of Legendrian links
… introduce new, readily computable invariants of Legendrian knots and links in standard contact three-space, allowing us to answer many previously open questions in contact knot theory. The origin of these invariants is the powerful Chekanov-Eliashberg differential graded algebra, which we …
-
Legendrian intersections in twisted 1-jet bundles
… long been settled, as has its contact analog for Legendrian intersections in the setting of 1-jet bundles with their standard contact structure. This latter result was due originally to Chekanov, and was later refined by Bhupal. More recently, Chantraine and Murphy proved an analog of the Arnold …
-
Immersed Lagrangian Fillings of Legendrian Submanifolds via Generating Families
<p>When a Legendrian sub manifold admits a generating family (GF), Sabloff and Traynor proved that there is an isomorphism between the GF-cohomology groups of the Legendrian and the cohomology groups of any GF-compatible embedded Lagrangian filling. In this paper, we show that a similar isomorphism …
-
Exact Lagrangian Fillings of Legendrian links and Weinstein 4-manifolds
… 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 links in the standard contact 3-sphere, and one can use …
-
A Product Structure on Generating Family Cohomology for Legendrian Submanifolds
<p>One way to obtain invariants of some Legendrian submanifolds in the standard contact manifolds of 1-jet spaces, J1M, is through the Morse theoretic technique of generating families. This dissertation extends the elective but not complete invariant of generating family cohomology by giving it a …
-
A Program to Visualize Legendrian Knots and Links from Generating Families
No abstract prepared.
-
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 …
-
Hypercube diagrams for knots, links, and knotted tori
… detects chirality are presented. There is also a Legendrian version of this invariant called the Legendrian cube number. We will show that the Legendrian cube number distinguishes the Legendrian left hand torus knots with maximal Thurston-Bennequin number and maximal rotation number from the …
-
Circle-Valued Generating Family Invariants
<p>Legendrian knot theory is the study of topological knots and links that satisfy an additional, geometric condition. This condition, imposed by a contact structure, makes it possible for certain knots to be topologically equivalent without being Legendrian equivalent. In recent years, real-valued …
-
Tight contact structures on small Seifert spaces
… small Seifert space and the contact framing of Legendrian vertical circles in it, and apply this relation to classify up to isotopy tight contact structures on small Seifert spaces with e₀ [not equal to] 0, -1, -2.
-
Ozsva?th-Szabo? invariants of contact surgeries
… what happens when doing contact surgeries along Legendrian links in S 3 : more specifically, I am going to look at contact manifolds through the eyes of Heegaard Floer homology, by computing their Ozsvath-Szab6 invariants. It's a classical result that doing negative contact surgeries along …
-
Scattering at threshold in massive wave propagation and ionization
In this thesis, we examine the transition between Legendrian regularity and ellipticity at infinity for two PDEs, the Schrödinger–Helmholtz equation with an attractive long range potential and the Klein–Gordon equation. In the former case, the transition occurs as the spectral parameter 𝐸 → 0⁺, and …
-
The Maximal Thurston-Bennequin Number on Grid Number n Diagrams
… upper bound for the Thurston-Bennequin number of Legendrian knots and links on a rectangular grid with arc index n.</p> <p>TB(n)=CR(n)-[n/2]</p> <p>In order to prove the bound, we will separate our work for when n is even and when n is odd. After we prove the upper bound, we will show that there …
-
Orderability and rigidity in contact geometry
… define a relative version of orderability for a Legendrian submanifold, and discuss the relationship between the two notions.</p>
-
A Tourist's Account of Characteristic Foliations on Convex Surfaces in 3-D Contact Geometry
… introduced next, concluding with an overview of Legendrian knots in contact 3-manifolds. Next, we develop a number of lemmas as tools for dealing with characteristic foliations, concluding with some sightseeing with regards to the theory of so-called "movies", allowing a glimpse into the workings …
-
Dynamical and Riemannian properties of Engel structures
… for a non-singular Morse-Smale field to be Legendrian with respect to a contact structure. Finally we study the holomorphic analogue of Engel structures and we produce an uncountable family of non-standard examples on C4. We do this by controlling the topology and the geometry of the space …
-
Pairs of geometric foliations of regular and singular surfaces
… curves. By considering cross-ratios of Legendrian lines in the manifold of contact elements to the surface we show that certain properties of the characteristic curves are invariant under projective transformations, and examine their behaviour at cusps of Gauss. We establish an analogy …