Jet spaces over Carnot groups

Jet spaces over Rn have been shown to have a canonical structure of strati-fied Lie groups (also known as Carnot groups). We construct jet spaces over stratified Lie groups adapted to horizontal differentiation and show that these jet spaces are themselves stratified Lie groups. Furthermore, we show that these jet spaces support a prolongation theory for contact maps, and in particular, a Backlund type theorem holds. A byproduct of these results is an embedding theorem that shows that every stratified Lie group of step s + 1 can be embedded in a jet space over a stratified Lie group of step s.