Jet spaces as nonrigid Carnot groups

Ben Warhurst

Abstract: We define a product on the jet spaces $J^k(\R^m,\R^n)$ which makes them Carnot groups. The Carnot group contact structure coincides with the classical contact structure in the Lie-Bäcklund setting. Therefore, by prolongation, they are nonrigid Carnot groups, meaning that the space of contact maps is infinite dimensional. We also show that strata dimensions are not rigidity invariants. This is demonstrated by constructing two distinct Carnot groups with strata dimensions $(3,2,1)$ but with opposite rigidity.

Classification (MSC2000): 53C24, 22E25

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