Representations of complex hyperbolic lattices into rank 2 classical Lie groups of Hermitian type
| dc.creator | Koziarz, Vincent | |
| dc.creator | Maubon, Julien | |
| dc.date | 2007-03-06 | |
| dc.date | 2007-03-07 | |
| dc.date.accessioned | 2026-07-07T07:50:28Z | |
| dc.date.available | 2026-07-07T07:50:28Z | |
| dc.description | Let G be either SU(p,2) with p>=2, Sp(2,R) or SO(p,2) with p>=3. The symmetric spaces associated to these G's are the classical bounded symmetric domains of rank 2, with the exceptions of SO*(8)/U(4) and SO*(10)/U(5). Using the correspondence between representations of fundamental groups of Kähler manifolds and Higgs bundles we study representations of uniform lattices of SU(m,1), m>1, into G. We prove that the Toledo invariant associated to such a representation satisfies a Milnor-Wood type inequality and that in case of equality necessarily G=SU(p,2) with p>=2m and the representation is reductive, faithful, discrete, and stabilizes a copy of complex hyperbolic space (of maximal possible induced holomorphic sectional curvature) holomorphically and totally geodesically embedded in the Hermitian symmetric space SU(p,2)/S(U(p)xU(2)), on which it acts cocompactly. | |
| dc.identifier | https://arxiv.org/abs/math/0703174 | |
| dc.identifier | http://arxiv.org/abs/math/0703174 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/125176 | |
| dc.subject | Differential Geometry | |
| dc.title | Representations of complex hyperbolic lattices into rank 2 classical Lie groups of Hermitian type | |
| dc.type | text |