On Double Vector Bundles

Abstract

In this paper, we construct a category of short exact sequences of vector bundles and prove that it is equivalent to the category of double vector bundles. Moreover, operations on double vector bundles can be transferred to operations on the corresponding short exact sequences. In particular, we study the duality theory of double vector bundles in term of the corresponding short exact sequences. Examples including the jet bundle and the Atiyah algebroid are discussed.

19 Pages

References in corpus (2)

• Higher vector bundles and multi-graded symplectic manifolds
• Lie algebroid structures on double vector bundles and representation theory of Lie algebroids