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

We present the notion of a filtered bundle as a generalisation of a non-negatively graded manifold. In particular, we weaken the necessity of the transformation laws for local coordinates to exactly respect the weight of the coordinates by allowing more general `filtered' transformation laws. The key examples of such bundles include affne bundles and various jet bundles, both of which play fundamental roles in geometric mechanics and field theory.