  Let $M$ be a connected 1-manifold, i.e., $M = \R \cong (0, 1), [0, 1), [0,
1]$, or $S^1$, and let $\Homeo_+(M)$ (resp. $\Diff_+^1(M)$) be the group of
orientation-preserving homeomorphisms (resp. $C^1$ diffeomorphisms) of $M$. It
is a classical result that if $N$ is a finitely-generated, torsion-free
nilpotent group, then there exist 1-1 homomorphisms $\phi\colon N \to
\Homeo_+(M)$. Farb and Franks show that, in fact, there exists a 1-1
homomorphism $N \to \Diff_+^1(M)$. In this paper we obtain a stronger result:
every action $\phi\colon N \to \Homeo_+(M)$ is topologically conjugate to an
action $\tilde{\phi}\colon N \to \Diff_+^1(M)$.

Dynamical Systems;Group Theory