Journal Articles Advances in Mathematics Year : 2025

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

Abstract

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.

Dates and versions

hal-04936419 , version 1 (08-02-2025)

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Hélène Eynard-Bontemps, Andrés Navas. The space of $C^{1+ac}$ actions of $\mathbb{Z}^d$ on a one-dimensional manifold is path-connected. Advances in Mathematics, 2025, 478, pp.110395. ⟨10.1016/j.aim.2025.110395⟩. ⟨hal-04936419⟩
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