TY - JOUR
T1 - Rozansky–Witten-Type Invariants from Symplectic Lie Pairs
AU - Voglaire, Yannick
AU - Xu, Ping
N1 - Publisher Copyright:
© 2014, Springer-Verlag Berlin Heidelberg.
PY - 2015/5
Y1 - 2015/5
N2 - 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.
AB - 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.
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U2 - 10.1007/s00220-014-2221-8
DO - 10.1007/s00220-014-2221-8
M3 - Article
AN - SCOPUS:84925510139
SN - 0010-3616
VL - 336
SP - 217
EP - 241
JO - Communications In Mathematical Physics
JF - Communications In Mathematical Physics
IS - 1
ER -