Kirill Mackenzie (University of Sheffield)
K.Mackenzie@sheffield.ac.uk When working with a Poisson manifold, one can use, for example, the bracket of functions, the 2-vector field, or the bracket of 1-forms. The latter is the Lie algebroid structure on the cotangent bundle. This viewpoint embeds Poisson geometry into a general and established framework, and --- despite the contravariance of T* --- allows various constructions to be seen as natural covariant processes. I will describe the effects of this formulation on the study of Poisson Lie groups and elsewhere.