Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

The canonical kappa involution for the iterated tangent bundle TTM has a surprising number of important applications and interesting generalizations. One can study the kappa map for M being a Lie groupoid. One can also look for generalizations to the higher order tangent bundles. These questions will be discussed in my talk which is partially based on my joint paper with Michał Jóźwikowski "Prototypes of higher algebroids with applications to variational calculus", arXiv:1306.3379.