Advanced Studies in Pure Mathematics

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

Shigenori Matsumoto

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

Denote by $\mathrm{Diff}_{c}^{r}(M)_{0}$ the identity component of the group of the compactly supported $C^{r}$ diffeomorphisms of a connected $C^{\infty}$ manifold $M$. We show that if $\dim(M)\geq2$ and $r\neq \dim(M)+1$, then any homomorphism from $\mathrm{Diff}_{c}^{r}(M)_{0}$ to $\mathrm{Diff}^{1}(\mathbb{R})$ or $\mathrm{Diff}^{1}(S^{1})$ is trivial.

Article information

Source
Geometry, Dynamics, and Foliations 2013: In honor of Steven Hurder and Takashi Tsuboi on the occasion of their 60th birthdays, T. Asuke, S. Matsumoto and Y. Mitsumatsu, eds. (Tokyo: Mathematical Society of Japan, 2017), 441-451

Dates
Received: 22 April 2014
Revised: 13 September 2014
First available in Project Euclid: 4 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1538671780

Digital Object Identifier
doi:10.2969/aspm/07210441

Mathematical Reviews number (MathSciNet)
MR3726723

Zentralblatt MATH identifier
1388.57027

Subjects
Primary: 57S05: Topological properties of groups of homeomorphisms or diffeomorphisms
Secondary: 22F05: General theory of group and pseudogroup actions {For topological properties of spaces with an action, see 57S20}

Keywords
group of diffeomorphisms action on the real line

Citation

Matsumoto, Shigenori. Actions of groups of diffeomorphisms on one-manifolds by $C^{1}$ diffeomorphisms. Geometry, Dynamics, and Foliations 2013: In honor of Steven Hurder and Takashi Tsuboi on the occasion of their 60th birthdays, 441--451, Mathematical Society of Japan, Tokyo, Japan, 2017. doi:10.2969/aspm/07210441. https://projecteuclid.org/euclid.aspm/1538671780


Export citation