Nilpotent pseudogroups of functions on an interval
Tania M. Begazo, Nicolau C. Saldanha
Abstract
A near-identity nilpotent pseudogroup of order m >= 1 is a family f1, ..., fn: (-1,1) -> R of C2 functions for which: |fi - id|C1 < epsilon for some small positive real number epsilon < 1/10m+1 and commutators of the functions fi 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 for nilpotent groups. As an application, we classify certain foliations of nilpotent manifolds.
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