Samuel Brady (University of Manchester)
samuel.brady@manchester.ac.uk
It is a classical result that a linear map of Lie algebras preserves brackets precisely when its dual is a Poisson map of Poisson manifolds. Higgins & Mackenzie proved an analogous result for Lie algebroids and Poisson bundles using comorphisms of Lie algebroids (a notion they introduced). In this talk, after reviewing these correspondences, we extend the duality to higher bracket structures (i.e. objects exhibiting L-infinity structure) by introducing the notion of an L-infinity comorphism. We conclude with some unresolved questions.