Nilpotent pseudogroups of functions on an interval

Abstract.

A near-identity nilpotent pseudogroup of order m ≥ 1 is a family f ₁, . . . , f _n : (-1, 1) → ℝ of C ² functions for which: ${\left| {f_{i} - {\text{id}}} \right|}_{{C^{1} }} < \in$ for some small positive real number ∈ < 1/10^m+1 and commutators of the functions f _i of order at least m equal the identity. We present a classification of near-identity nilpotent pseudogroups: our results are similar to those of Plante, Thurston, Farb and Franks. As an application, we classify certain foliations of nilpotent manifolds.