Communications in Mathematical Physics

, Volume 336, Issue 1, pp 217–241 | Cite as

Rozansky–Witten-Type Invariants from Symplectic Lie Pairs

  • Yannick Voglaire
  • Ping XuEmail author


We introduce symplectic structures on “Lie pairs” of (real or complex) Lie algebroids as studied by Chen et al. (From Atiyah classes to homotopy Leibniz algebras. arXiv:1204.1075, 2012), 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.


Symplectic Structure Weight System Nilpotent Orbit Chord Diagram Trivalent Graph 
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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Mathematics Research UnitUniversity of LuxembourgKirchbergLuxembourg
  2. 2.Department of MathematicsPenn State UniversityUniversity ParkUSA

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