4 papers
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…
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…