Duality and triple structures

Details Duality and triple structures Duality and triple structures

2004-06-14

arxiv.org/abs/math/0406267v1

Mathematics

Symplectic Geometry

28 pages. Accepted for the Birkhauser volume of articles dedicated to Alan Weinstein on the occasion of his 60th birthday, and

Scientific paper

We first recall the basic theory of double vector bundles and the canonical pairing of their duals introduced by the author and by Konieczna and Urbanski. We then show that the relationship between a double vector bundle and its two duals can be understood simply in terms of an associated cotangent triple vector bundle. In particular we show that the dihedral group of the triangle acts on this triple via forms of the isomorphisms R introduced by the author and Ping Xu. We then consider the three duals of a general triple vector bundle and show that the corresponding group is neither the dihedral group of the square nor the symmetry group on four symbols.

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