7 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…
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…
Perverse Microsheaves
Laurent Côté, Christopher Kuo, David Nadler +1
On a complex contact manifold, or complex symplectic manifold with weight-1 circle action, we construct a sheaf of stable categories carrying a t-structure which is locally equival…
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…
Microsheaves from Hitchin fibers via Floer theory
Vivek Shende
Fix a non-stacky component of the moduli of stable Higgs bundles, on which the Hitchin fibration is proper. We show that any smooth Hitchin fiber determines a microsheaf on the glo…
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…