Critical regularity of nilpotent groups acting on one-dimensional compact manifolds
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866918416949968896 |
|---|---|
| author | Escayola, Maximiliano Kleptsyn, Victor |
| author_facet | Escayola, Maximiliano Kleptsyn, Victor |
| contents | Given a finitely generated, torsion-free nilpotent group, we find the maximum possible (critical) regularity for its faithful actions by diffeomorphisms of the closed or half-open interval and of the circle. Our result gives an expression for its value in purely algebraic terms (using the relative growth of appropriate subgroups), generalizing many preceding works. As an intermediate step, we generalize the Bass-Guivarc'h formula, obtaining a formula for the relative growth of subgroups of nilpotent groups, as well as for the growth of the corresponding Schreier graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28185 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Critical regularity of nilpotent groups acting on one-dimensional compact manifolds Escayola, Maximiliano Kleptsyn, Victor Dynamical Systems Group Theory 20F18, 37C05, 37C85, 37E05 Given a finitely generated, torsion-free nilpotent group, we find the maximum possible (critical) regularity for its faithful actions by diffeomorphisms of the closed or half-open interval and of the circle. Our result gives an expression for its value in purely algebraic terms (using the relative growth of appropriate subgroups), generalizing many preceding works. As an intermediate step, we generalize the Bass-Guivarc'h formula, obtaining a formula for the relative growth of subgroups of nilpotent groups, as well as for the growth of the corresponding Schreier graphs. |
| title | Critical regularity of nilpotent groups acting on one-dimensional compact manifolds |
| topic | Dynamical Systems Group Theory 20F18, 37C05, 37C85, 37E05 |
| url | https://arxiv.org/abs/2603.28185 |