Actions of groups of diffeomorphisms on one-manifolds

Abstract

Denote by $\DC(M)_0$ the identity component of the group of compactly supported $C^{\infty }$ diffeomorphisms of a connected $C^{\infty }$ manifold $M$, and by $\HR$ the group of the homeomorphisms of $\mathbb{R}$. We show that if $M$ is a closed manifold which fibers over $S^m$ ($m\ge 2$), then any homomorphism from $\DC(M)_0$ to $\HR$ is trivial.

This paper is withdrawn because there is a fatal error in the proof of the main theorem