On curves and jets of curves on supermanifolds

My work on curves and higher tangent bundles on supermanifolds has now been published as “On curves and jets of curves on supermanifolds“, Archivum mathematicum, Volume 50 (2014), No. 2.

In this paper we examine a natural concept of a curve on a supermanifold and the subsequent notion of the jet of a curve. We then tackle the question of geometrically defining the higher order tangent bundles of a supermanifold. Finally we make a quick comparison with the notion of a curve presented here are other common notions found in the literature.

The main idea was to try to follow the classical definitions of a curve, jets of curves at a point and the geometric or kinematic definition of higher tangent bundles. One of the complications in the superworld is that supermanifolds are not just set theoretical objects. To overcome this the more categorical set-up of the “functor of points” and “internal Homs” is needed.

I posted a little about this before here.