The space of $C^{1+ac}$ actions of $\mathbb{Z}^d$ on a one-dimensional manifold is path-connected
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913278765039616 |
|---|---|
| author | Eynard-Bontemps, Hélène Navas, Andrés |
| author_facet | Eynard-Bontemps, Hélène Navas, Andrés |
| contents | We show path-connectedness for the space of $\mathbb{Z}^d$ actions by $C^1$ diffeomorphisms with absolutely continuous derivative on both the closed interval and the circle. We also give a new and short proof of the connectedness of the space of $\mathbb{Z}^d$ actions by $C^2$ diffeomorphisms on the interval, as well as an analogous result in the real-analytic setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_17731 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The space of $C^{1+ac}$ actions of $\mathbb{Z}^d$ on a one-dimensional manifold is path-connected Eynard-Bontemps, Hélène Navas, Andrés Dynamical Systems Functional Analysis Geometric Topology 37C05, 37C10, 37C15, 37E05, 37E10, 57S25 We show path-connectedness for the space of $\mathbb{Z}^d$ actions by $C^1$ diffeomorphisms with absolutely continuous derivative on both the closed interval and the circle. We also give a new and short proof of the connectedness of the space of $\mathbb{Z}^d$ actions by $C^2$ diffeomorphisms on the interval, as well as an analogous result in the real-analytic setting. |
| title | The space of $C^{1+ac}$ actions of $\mathbb{Z}^d$ on a one-dimensional manifold is path-connected |
| topic | Dynamical Systems Functional Analysis Geometric Topology 37C05, 37C10, 37C15, 37E05, 37E10, 57S25 |
| url | https://arxiv.org/abs/2306.17731 |