Rozansky–Witten-Type Invariants from Symplectic Lie Pairs

Yannick Voglaire, Ping Xu

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 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.

Original languageEnglish (US)
Pages (from-to)217-241
Number of pages25
JournalCommunications In Mathematical Physics
Volume336
Issue number1
DOIs
StatePublished - Jan 1 2015

Fingerprint

Symplectic Manifold
Chord Diagrams
Leibniz Algebra
Lie Algebroids
Three-manifolds
Michael Francis Atiyah
Invariant
Symplectic Structure
Homotopy
Knot
algebra
diagrams
Class

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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Rozansky–Witten-Type Invariants from Symplectic Lie Pairs. / Voglaire, Yannick; Xu, Ping.

In: Communications In Mathematical Physics, Vol. 336, No. 1, 01.01.2015, p. 217-241.

Research output: Contribution to journalArticle

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