Groups of diffeomorphisms of one-manifolds, III: Nilpotent subgroups

Abstract

Plante-Thurston proved that every nilpotent subgroup of $\Diff^2(S^1)$ is abelian. One of our main results is a sharp converse: $\Diff^1(S^1)$ contains every finitely-generated, torsion-free nilpotent group.

This is a revision of a paper published in 2003. It corrects a minor mistake ( "2n-2j+2" changed to "4n-2j+2") in the proof of the Theorem 1.1. See Remark 2.1 in the current version