31 citations · 113 across the 16 of their papers we have counts for
17 papers
Lagrangian Zigzag Cobordisms
Joshua M. Sabloff, David Shea Vela-Vick, C. -M. Michael Wong +1
We investigate an equivalence relation on Legendrian knots in the standard contact three-space defined by the existence of an interpolating zigzag of Lagrangian cobordisms. We comp…
Upper bounds for the Lagrangian cobordism relation on Legendrian links
Joshua M. Sabloff, David Shea Vela-Vick, C. -M. Michael Wong
Lagrangian cobordism induces a preorder on the set of Legendrian links in any contact 3-manifold. We show that any finite collection of null-homologous Legendrian links in a tight…
Ribbon homology cobordisms
Aliakbar Daemi, Tye Lidman, David Shea Vela-Vick +1
We study 4-dimensional homology cobordisms without 3-handles, showing that they interact nicely with Thurston geometries, character varieties, and instanton and Heegaard Floer homo…
An unoriented skein relation via bordered-sutured Floer homology
David Shea Vela-Vick, C. -M. Michael Wong
We show that the bordered-sutured Floer invariant of the complement of a tangle in an arbitrary 3-manifold , with minimal conditions on the bordered-sutured structure, satisfies…
A note on the knot Floer homology of fibered knots
John A. Baldwin, David Shea Vela-Vick
We prove that the knot Floer homology of a fibered knot is nontrivial in its next-to-top Alexander grading. Immediate applications include new proofs of Krcatovich's result that kn…
Lifting Lagrangian immersions in to Lagrangian cones in
Scott Baldridge, Ben McCarty, David Shea Vela-Vick
In this paper we show how to lift Lagrangian immersions in to produce Lagrangian cones in , and use this process to produce several families of…
Transverse braids and combinatorial knot Floer homology
Peter Lambert-Cole, David Shea Vela-Vick
We describe a new method for combinatorially computing the transverse invariant in knot Floer homology. Previous work of the authors and Stone used braid diagrams to combinatoriall…
Sutured Floer homology and invariants of Legendrian and transverse knots
John B. Etnyre, David Shea Vela-Vick, Rumen Zarev
Using contact-geometric techniques and sutured Floer homology, we present an alternate formulation of the minus and plus version of knot Floer homology. We further show how natural…
Braids and combinatorial knot Floer homology
Peter Lambert-Cole, Michaela Stone, David Shea Vela-Vick
We present a braid-theoretic approach to combinatorially computing knot Floer homology. To a knot or link K, which is braided about the standard disk open book decomposition for (S…
Generalized Gauss maps and integrals for three-component links: toward higher helicities for magnetic fields and fluid flows, Part 2
Dennis DeTurck, Herman Gluck, Rafal Komendarczyk +4
We describe a new approach to triple linking invariants and integrals, aiming for a simpler, wider and more natural applicability to the search for higher order helicities of fluid…
On the equivalence of Legendrian and transverse invariants in knot Floer homology
John A. Baldwin, David Shea Vela-Vick, Vera Vertesi
Using the grid diagram formulation of knot Floer homology, Ozsvath, Szabo and Thurston defined an invariant of transverse knots in the tight contact 3-sphere. Shortly afterwards, L…
Pontryagin invariants and integral formulas for Milnor's triple linking number
Dennis DeTurck, Herman Gluck, Rafal Komendarczyk +3
To each three-component link in the 3-sphere, we associate a geometrically natural characteristic map from the 3-torus to the 2-sphere, and show that the pairwise linking numbers a…
Legendrian contact homology and nondestabilizability
Clayton Shonkwiler, David Shea Vela-Vick
We provide the first example of a Legendrian knot with nonvanishing contact homology whose Thurston-Bennequin invariant is not maximal.
Torsion and Open Book Decompositions
John B. Etnyre, David Shea Vela-Vick
We show that if (B,π) is an open book decomposition of a contact 3-manifold (Y,ξ), then the complement of the binding B has no Giroux torsion. We also prove the sutured Heegaard-Fl…
Triple linking numbers, ambiguous Hopf invariants and integral formulas for three-component links
Dennis DeTurck, Herman Gluck, Rafal Komendarczyk +3
Three-component links in the 3-dimensional sphere were classified up to link homotopy by John Milnor in his senior thesis, published in 1954. A complete set of invariants is given…
On the transverse invariant for bindings of open books
David Shea Vela-Vick
Consider a transverse knot which is the binding of an open book for the ambient contact manifold. In this paper, we show that the transverse invariants defined by Lisca, Ozsvath, S…
Higher-dimensional linking integrals
Clayton Shonkwiler, David Shea Vela-Vick
We derive an integral formula for the linking number of two submanifolds of the n-sphere S^n, of the product S^n x R^m, and of other manifolds which appear as "nice" hypersurfaces…