Rozansky--Witten-type invariants from symplectic Lie pairs
Speaker: Yannick Voglaire, University of Luxembourg
Abstract: In 1997, Rozansky and Witten built new finite-type invariants of 3-manifolds from hyperkahler manifolds. It was later shown by Kontsevich and Kapranov that those invariants only depend on the holomorphic symplectic structure of the hyperkahler manifolds. Indeed Kapranov proved that these invariants may be built from only two objects: the Atiyah class of the underlying complex manifold, and the holomorphic symplectic form. In this talk, we introduce symplectic structures on "Lie pairs" of (real or complex) algebroids, encompassing homogeneous symplectic spaces, symplectic manifolds with a $\mathfrak g$-action and holomorphic symplectic manifolds. We show that to each such symplectic Lie pair are associated Rozansky-Witten-type invariants of three-manifolds and knots, given respectively by weight systems on trivalent and chord diagrams. In this talk, I will review the necessary notions to state the result and explain the construction of the weight systems.
Room Reservation Information
Room Number: 106 McAllister
Time: 2:30pm - 3:30pm