Actions of groups of diffeomorphisms on one-manifolds by $C^1$ diffeomorphisms

Abstract

Denote by $\DC(M)_0$ the identity component of the group of the compactly supported $C^r$ diffeomorphisms of a connected $C^{\infty }$ manifold $M$. We show that if $\dim (M)\ge 2$ and $r\ne \dim (M)+1$, then any homomorphism from $\DC(M)_0$ to ${\Diff}^1(\R)$ or ${\Diff}^1(S^1)$ is trivial.

8 pages. arXiv admin note: text overlap with arXiv:1308.5381