Nilpotent pseudogroups of functions on an interval

Details Nilpotent pseudogroups of functions on an interval Nilpotent pseudogroups of functions on an interval

2004-04-07

arxiv.org/abs/math/0404157v2

Bull Braz Math Soc, New Series 36(1), 25-38 (2005)

Mathematics

Dynamical Systems

13 pages, no figures

Scientific paper

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: |f_i - id|_{C^1} < epsilon for some small positive real number epsilon < 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 for nilpotent groups. As an application, we classify certain foliations of nilpotent manifolds.

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