The space of $C^{1+ac}$ actions of $\mathbb{Z}^d$ on a one-dimensional manifold is path-connected

Fuente: arXiv
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Main Authors: Eynard-Bontemps, Hélène, Navas, Andrés
Format: Preprint
Published: 2023
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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