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

Publication date: 23 February 2018

Abstract: Denote by

D C (M)_{0}

the identity component of the group of the compactly supported

C^{r}

diffeomorphisms of a connected

C^{i} n f t y

manifold

M

. We show that if

d i m (M) g e q 2

and

r e q d i m (M) + 1

, then any homomorphism from

D C (M)_{0}

to

{D i f f}^{1} (R)

or

{D i f f}^{1} (S^{1})

is trivial.