On certain canonical diffeomorphisms in symplectic and Poisson geometry

Details On certain canonical diffeomorphisms in symplectic and Poisson geometry On certain canonical diffeomorphisms in symplectic and Poisson geometry

2002-10-24

arxiv.org/abs/math/0210384v1

Mathematics

Differential Geometry

12 pages. To appear in `Quantization, Poisson brackets and beyond', proceedings of a conference at UMIST (UK) in July 2001, ed

Scientific paper

The canonical involution of a double (=iterated) tangent bundle may be dualized in different ways to yield relations between the Tulczyjew diffeomorphism, the Poisson anchor associated with the standard symplectic structure on the cotangent space,and the reversal diffeomorphism. We show that the constructions which yield these maps extend very generally to the double Lie algebroids of double Lie groupoids, where they play a crucial role in the relations between double Lie algebroids and Lie bialgebroids.

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