The Division Map of Principal Bundles with Groupoid Structure and Generalized Gauge Transformations

Motivated by the computations done in [9], where I introduced and discussed what I called the groupoid of generalized gauge transformations, viewed as a groupoid over the objects of the category BunG,M of principal G-bundles over a given manifold M , I develop in this paper the same ideas for the more general case of principal G-bundles or principal bundles with structure groupoid G, where now G is a Lie groupoid in the sense of [7]. Most of the concepts introduced in [9] can be translated almost verbatim in the framework of principal bundles with structure groupoid G; in particular, the key rôle for the construction of generalized gauge transformations is again played by (the equivalent in the framework of principal bundles with groupoid structure of) the division map φP . Of great importance are also the generalized conjugation in a groupoid and the concept of (twisted) equivariant maps between groupoid-spaces.