I gave a talk at the Working Seminar in Geometry and Analysis a couple of weeks ago and have now written up and posted the notes for the talk.

Abstract: A sub-Riemannian manifold models constrained motion through a choice of a "horizontal distribution" on the tangent bundle. The standard denitions of tangent space and the dierential of a smooth map break down in this setting. Following papers by Bellaiche and Ponge, I will discuss the way these notions are replaced by talking about non-abelian vector spaces (Carnot groups) and induced maps between them.