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Rozansky–Witten-Type Invariants from Symplectic Lie Pairs

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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.

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Authors and Affiliations

  1. Mathematics Research Unit, University of Luxembourg, Kirchberg, Luxembourg

    Yannick Voglaire

  2. Department of Mathematics, Penn State University, University Park, PA, USA

    Ping Xu

Authors
  1. Yannick Voglaire
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  2. Ping Xu
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Correspondence to Ping Xu.

Additional information

Communicated by H. Ooguri

Y. Voglaire’s research was partially supported by the Fonds National de la Recherche, Luxembourg, through the AFR Grant PDR 2012-1 (Project Reference 3966341).

P. Xu’s research was partially supported by the National Science Foundation Grant DMS-1101827.

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Voglaire, Y., Xu, P. Rozansky–Witten-Type Invariants from Symplectic Lie Pairs. Commun. Math. Phys. 336, 217–241 (2015). https://doi.org/10.1007/s00220-014-2221-8

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