Boundary actions by higher-rank lattices: Classification and embedding in low dimensions, local rigidity, smooth factors
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917681665409024 |
|---|---|
| author | Brown, Aaron Hertz, Federico Rodriguez Wang, Zhiren |
| author_facet | Brown, Aaron Hertz, Federico Rodriguez Wang, Zhiren |
| contents | We study actions by lattices in higher-rank (semi)simple Lie groups on compact manifolds. By classifying certain measures invariant under a related higher-rank abelian action (the diagonal action on the suspension space) we deduce a number of new rigidity results related to standard projective actions (i.e. boundary actions) by such groups.
Specifically, in low dimensions we show all actions (with infinite image) are conjugate to boundary actions. We also show standard boundary actions (e.g. projective actions on generalized flag varieties) are local rigid and classify all smooth actions that are topological factors of such actions. Finally, for volume-preserving actions in low dimensions (with infinite image) we provide a mechanism to detect the presence of "blow-ups" for the action by studying measures that are $P$-invariant but not $G$-invariant for the suspension action. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16202 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Boundary actions by higher-rank lattices: Classification and embedding in low dimensions, local rigidity, smooth factors Brown, Aaron Hertz, Federico Rodriguez Wang, Zhiren Dynamical Systems We study actions by lattices in higher-rank (semi)simple Lie groups on compact manifolds. By classifying certain measures invariant under a related higher-rank abelian action (the diagonal action on the suspension space) we deduce a number of new rigidity results related to standard projective actions (i.e. boundary actions) by such groups. Specifically, in low dimensions we show all actions (with infinite image) are conjugate to boundary actions. We also show standard boundary actions (e.g. projective actions on generalized flag varieties) are local rigid and classify all smooth actions that are topological factors of such actions. Finally, for volume-preserving actions in low dimensions (with infinite image) we provide a mechanism to detect the presence of "blow-ups" for the action by studying measures that are $P$-invariant but not $G$-invariant for the suspension action. |
| title | Boundary actions by higher-rank lattices: Classification and embedding in low dimensions, local rigidity, smooth factors |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2405.16202 |