Link homology from a stack of D2 branes with a B-twist

Abstract: This is a joint work with A. Oblomkov. The HOMFLY-PT polynomial invariant of a link in S^3 is `a sibling' of the DT invariant of a Calabi-Yau 3-fold X: the difference is that the HOMFLY-PT polynomial counts the curves in X in the presence of special Lagrangian submanifolds related to link components. We construct a categorification of the HOMFLY-PT polynomial based on a particular way of curve counting, when the curves are almost coincident and one has to account for their joint vibrations in a transverse C^2. Thus we select a special object FL in a 2-category associated with the Hilbert scheme of n points in C^2, define a homomorphism from the n-strand braid group to the monoidal category End(FL) and use it to associate a graded vector space (homology) to the closure of a braid. I will explain the details of the mathematical construction and its interpretation within the M-theory.

algebraic geometrysymplectic geometry

Audience: researchers in the topic

M-seminar