Nilpotent pseudogroups of functions on an interval

2004/04/30 by Tania M. Begazo, Nicolau C. Saldanha · 1 citation
Mathematics · #math.DS #math.GT #msc:37E05 #msc:37E45 #msc:57S25 #msc:57R30

paper · pdf

published as Bull Braz Math Soc, New Series 36(1), 25-38 (2005) · 13 pages, no figures

arxiv created 2004/11/22 · arxiv updated 2009/12/01

Abstract

A near-identity nilpotent pseudogroup of order m >= 1 is a family f₁, ..., f_n: (-1,1) -> R of C² functions for which: |f_i - id|_C¹ < 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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