Rozansky-Witten-type invariants from symplectic Lie pairs

17 Jan 2015  ·  Voglaire Yannick, Xu Ping ·

We introduce symplectic structures on "Lie pairs" of (real or complex) algebroids as studied by Chen, Stienon and the second author (From Atiyah classes to homotopy Leibniz algebras, arXiv:1204.1075), 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...

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Differential Geometry High Energy Physics - Theory Algebraic Geometry Quantum Algebra