Global Rigidity of Codimension One Actions
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914174957780992 |
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| author | Serrato, Camilo Arosemena |
| author_facet | Serrato, Camilo Arosemena |
| contents | Consider a smooth, locally free, codimension-one action of a higher-rank, simple, split Lie group $G$ on a closed manifold $M$. Let $P$ be a minimal parabolic subgroup of $G$. If the action admits a $P$-invariant probability measure that is mixing, then the action is either equivariantly diffeomorphic to the suspension of a codimension one, locally free action on a closed manifold of a parabolic subgroup of $G$; or, it is finitely and equivariantly covered by the action of $G$ on $G/Γ\times S^1$, where the action on $G/Γ$ is the coset action, and $G$ acts trivially on $S^1$. We prove this by doing a jointly integration argument of stable and center unstable Pesin manifolds. This is a smooth version of results by Nevo and Zimmer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_00842 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global Rigidity of Codimension One Actions Serrato, Camilo Arosemena Dynamical Systems Consider a smooth, locally free, codimension-one action of a higher-rank, simple, split Lie group $G$ on a closed manifold $M$. Let $P$ be a minimal parabolic subgroup of $G$. If the action admits a $P$-invariant probability measure that is mixing, then the action is either equivariantly diffeomorphic to the suspension of a codimension one, locally free action on a closed manifold of a parabolic subgroup of $G$; or, it is finitely and equivariantly covered by the action of $G$ on $G/Γ\times S^1$, where the action on $G/Γ$ is the coset action, and $G$ acts trivially on $S^1$. We prove this by doing a jointly integration argument of stable and center unstable Pesin manifolds. This is a smooth version of results by Nevo and Zimmer. |
| title | Global Rigidity of Codimension One Actions |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2512.00842 |