75 citations · 554 across the 50 of their papers we have counts for
38 papers · 1 filter
Ghost bubble censorship
Tobias Ekholm, Vivek Shende
When a Gromov limit of embedded holomorphic curves is constant on some component of the domain, the non-collapsed component must exhibit some degenerate behavior at the attaching p…
Chekanov-Eliashberg dg-algebras for singular Legendrians
Johan Asplund, Tobias Ekholm
The Chekanov-Eliashberg dg-algebra is a holomorphic curve invariant associated to Legendrian submanifolds of a contact manifold. We extend the definition to Legendrian embeddings o…
Colored HOMFLYPT counts holomorphic curves
Tobias Ekholm, Vivek Shende
We compute the contribution of all multiple covers of an isolated rigid embedded holomorphic annulus, stretching between Lagrangians, to the skein-valued count of open holomorphic…
Skein recursion for holomorphic curves and invariants of the unknot
Tobias Ekholm, Vivek Shende
We determine the skein-valued Gromov-Witten partition function for a single toric Lagrangian brane in or the resolved conifold. We first show geometrically they must…
Augmentations, annuli, and Alexander polynomials
Luís Diogo, Tobias Ekholm
The augmentation variety of a knot is the locus, in the 3-dimensional coefficient space of the knot contact homology dg-algebra, where the algebra admits a unital chain map to the…
Holomorphic curves for Legendrian surgery
Tobias Ekholm
Let be a Weinstein manifold with ideal contact boundary . If is a link of Legendrian spheres in then by attaching Weinstein handles to along we get…
Skeins on Branes
Tobias Ekholm, Vivek Shende
We study 1-parameter families of holomorphic curves with Lagrangian boundary in Calabi-Yau 3-folds. We show that the expected codimension one phenomena can be organized to match th…
Refined disk potentials for immersed Lagrangian surfaces
Georgios Dimitroglou Rizell, Tobias Ekholm, Dmitry Tonkonog
We define a refined Gromov-Witten disk potential of self-transverse monotone immersed Lagrangian surfaces in a symplectic 4-manifold as an element in a capped version of the Chekan…
Higher genus knot contact homology and recursion for colored HOMFLY-PT polynomials
Tobias Ekholm, Lenhard Ng
We sketch a construction of Legendrian Symplectic Field Theory (SFT) for conormal tori of knots and links. Using large duality and Witten's connection between open Gromov-Witte…
Lagrangian fillings and complicated Legendrian unknots
Sylvain Courte, Tobias Ekholm
An exact Lagrangian submanifold in the symplectization of standard contact -space with Legendrian boundary can be glued to itself along . This gives a Legendrian…
Knot contact homology and open Gromov-Witten theory
Tobias Ekholm
Knot contact homology studies symplectic and contact geometric properties of conormals of knots in 3-manifolds using holomorphic curve techniques. It has connections to both mathem…
Duality between Lagrangian and Legendrian invariants
Tobias Ekholm, Yanki Lekili
Consider a pair , of a Weinstein manifold with an exact Lagrangian submanifold , with ideal contact boundary , where is a contact manifold and …
Nearby Lagrangian fibers and Whitney sphere links
Tobias Ekholm, Ivan Smith
Let n>3, and let L be a Lagrangian embedding of an n-disk into the cotangent bundle of n-dimensional Euclidean space that agrees with the cotangent fiber over a non-zero point x ou…
A complete knot invariant from contact homology
Tobias Ekholm, Lenhard Ng, Vivek Shende
We construct an enhanced version of knot contact homology, and show that we can deduce from it the group ring of the knot group together with the peripheral subgroup. In particular…
Knot contact homology, string topology, and the cord algebra
Kai Cieliebak, Tobias Ekholm, Janko Latschev +1
The conormal Lagrangian of a knot in is the submanifold of the cotangent bundle consisting of covectors along that annihilate tangen…
Symplectic and contact differential graded algebras
Tobias Ekholm, Alexandru Oancea
We define Hamiltonian simplex differential graded algebras (DGA) with differentials that deform the high energy symplectic homology differential and wrapped Floer homology differen…
Lagrangian exotic spheres
Tobias Ekholm, Thomas Kragh, Ivan Smith
Let k>2. We prove that the cotangent bundles of oriented homotopy (2k-1)-spheres S and S' are symplectomorphic only if the classes defined by S and S' agree up to sign in the quoti…
Non-loose Legendrian spheres with trivial Contact Homology DGA
Tobias Ekholm
Loose Legendrian n-submanifolds, for n at least 2, were introduced by Murphy and proved to be flexible in the h-principle sense: any two loose Legendrian submanifolds that are form…
Notes on topological strings and knot contact homology
Tobias Ekholm
We give an introduction to the physics and mathematics involved in the recently observed relation between topological string theory and knot contact homology and then discuss this…
Legendrian contact homology in the boundary of a subcritical Weinstein 4-manifold
Tobias Ekholm, Lenhard Ng
We give a combinatorial description of the Legendrian contact homology algebra associated to a Legendrian link in or any connected sum , viewed…
Constructing exact Lagrangian immersions with few double points
Tobias Ekholm, Yakov Eliashberg, Emmy Murphy +1
We establish an -principle for exact Lagrangian immersions with transverse self-intersections and the minimal, or near-minimal number of double points. One corollary of our resu…
Legendrian knots and exact Lagrangian cobordisms
Tobias Ekholm, Ko Honda, Tamás Kálmán
We introduce constructions of exact Lagrangian cobordisms with cylindrical Legendrian ends and study their invariants which arise from Symplectic Field Theory. A pair consi…
Exact Lagrangian immersions with one double point revisited
Tobias Ekholm, Ivan Smith
We study exact Lagrangian immersions with one double point of a closed orientable manifold K into n-complex-dimensional Euclidean space. Our main result is that if the Maslov gradi…
Exact Lagrangian immersions with a single double point
Tobias Ekholm, Ivan Smith
Let k > 2. We show that if a closed orientable 2k-manifold K, with Euler characteristic not equal to -2, admits an exact Lagrangian immersion into complex Euclidean 2k-space with o…