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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.00842 |
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Table of 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.