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Seminar by Yannick Voglaire (Luxembourg)

Title: Rozansky--Witten-type invariants from symplectic Lie pairs

2014.03.20 | Christine Dilling

Date Wed 07 May
Time 15:15 16:15
Location Aud D.3

In 1997, Rozansky and Witten built new finite-type invariants of 3-manifolds from hyperkahler manifolds. It was later shown by Kapranov that those invariants only depend on the holomorphic symplectic structure of the hyperkahler manifolds, and may be built from only two objects: the Atiyah class of the underlying complex manifold, and the holomorphic symplectic form.

With Ping Xu, we introduce symplectic structures on "Lie pairs" of (real or complex) algebroids as studied by Chen-Stiénon-Xu, encompassing homogeneous symplectic spaces, symplectic manifolds with a 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.