تقرير
The space of $C^{1+ac}$ actions of $\mathbb{Z}^d$ on a one-dimensional manifold is path-connected
| العنوان: | The space of $C^{1+ac}$ actions of $\mathbb{Z}^d$ on a one-dimensional manifold is path-connected |
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| المؤلفون: | Eynard-Bontemps, Hélène, Navas, Andrés |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Dynamical Systems, Mathematics - Functional Analysis, Mathematics - Geometric Topology, 37C05, 37C10, 37C15, 37E05, 37E10, 57S25 |
| الوصف: | 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. Comment: 57 pages, 7 figures. This article improves and simplifies the results of arXiv:2103.06940, which will thus remain unpublished. This version contains a new Appendix in collaboration with Th\'eo Virot concerning a general discussion on the topology of low-regular diffeomorphism groups and a technical lemma of analysis |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2306.17731 |
| رقم الأكسشن: | edsarx.2306.17731 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |