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 $\R$. We show that if $M$ is a closed manifold which fibers over $S^m$ ($m\geq 2$), then any homomorphism from $\DC(M)_0$ to $\HR$ is trivial.