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

Graded bundles are a particularly nice 'species' of graded manifolds that can be thought of as a generalisation vector bundles. We define the notion of a weighted A-connection, where A is a Lie algebroid. One should view weighted connections as respecting the graded structure just as linear connections respect the linear structure of a vector bundle. We will discuss the existence of such adapted connections and use them to define (quasi-)actions of Lie algebroids on graded bundles.