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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
Article

Abstract

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.

Keywords

Symplectic Structure Weight System Nilpotent Orbit Chord Diagram Trivalent Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© 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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