Local quaternionic rigidity for complex hyperbolic lattices
| dc.creator | Inkang, Kim | |
| dc.creator | Klingler, Bruno | |
| dc.creator | Pansu, Pierre | |
| dc.date | 2009-03-22 | |
| dc.date.accessioned | 2026-07-07T12:55:34Z | |
| dc.date.available | 2026-07-07T12:55:34Z | |
| dc.description | Let $Γ\stackrel{i}{\hookrightarrow} L$ be a lattice in the real simple Lie group $L$. If $L$ is of rank at least 2 (respectively locally isomorphic to $Sp(n,1)$) any unbounded morphism $ρ: Γ\longrightarrow G$ into a simple real Lie group $G$ essentially extends to a Lie morphism $ρ_L: L \longrightarrow G$ (Margulis's superrigidity theorem, respectively Corlette's theorem). In particular any such morphism is infinitesimally, thus locally, rigid. On the other hand, for $L=SU(n,1)$, even morphisms of the form $ρ: Γ\stackrel{i}{\hookrightarrow} L \longrightarrow G$ are not infinitesimally rigid in general. Almost nothing is known about their local rigidity. In this paper we prove that any {\em cocompact} lattice $Γ$ in SU(n,1) is essentially locally rigid (while in general not infinitesimally rigid) in the quaternionic groups $Sp(n,1)$, SU(2n,2) or SO(4n,4) (for the natural sequence of embeddings $SU(n,1) \subset Sp(n,1) \subset SU(2n,2) \subset SO(4n,4))$. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/0903.3706 | |
| dc.identifier | http://arxiv.org/abs/0903.3706 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/224290 | |
| dc.subject | Differential Geometry | |
| dc.subject | 14D07;20G10;20G20;32L20;53C24;53C26;53C35;53C43;53C55 | |
| dc.title | Local quaternionic rigidity for complex hyperbolic lattices | |
| dc.type | text |