6 papers
Open strings on knot complements
Sachin Chauhan, Tobias Ekholm, Pietro Longhi
Using skein valued holomorphic curve counting techniques, we give a flow loop formula for the skein valued partition function of the Lagrangian knot complement of a fibered knot (o…
Skein traces from curve counting
Tobias Ekholm, Pietro Longhi, Sunghyuk Park +1
Given a 3-manifold , and a branched cover arising from the projection of a Lagrangian 3-manifold in the cotangent bundle of to the zero-section, we define a map from the…
The skein valued mirror of the topological vertex
Tobias Ekholm, Pietro Longhi, Vivek Shende
We count holomorphic curves in complex 3-space with boundaries on three special Lagrangian solid tori. The count is valued in the HOMFLYPT skein module of the union of the tori. Us…
Legendrian surgery
Tobias Ekholm
This is an overview paper that describes Eliashberg's Legendrian surgery approach to wrapped Floer cohomology and use it to derive the basic relations between various holomorphic c…
The worldsheet skein D-module and basic curves on Lagrangian fillings of the Hopf link conormal
Tobias Ekholm, Pietro Longhi, Lukas Nakamura
HOMFLYPT polynomials of knots in the 3-sphere in symmetric representations satisfy recursion relations. Their geometric origin is holomorphic curves at infinity on knot conormals t…
Counting bare curves
Tobias Ekholm, Vivek Shende
We construct a class of perturbations of the Cauchy-Riemann equations for maps from curves to a Calabi-Yau threefold. Our perturbations vanish on components of zero symplectic area…