Geometric dimension of lattices in classical simple Lie groups

Javier Aramayona (1, 2) , Dieter Degrijse (3) , Conchita Martinez-Perez (4) , Juan Souto (5)

1 UAM - Universidad Autónoma de Madrid
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 NUI Galway - National University of Ireland [Galway]
4 University of Zaragoza - Universidad de Zaragoza [Zaragoza]
5 IRMAR - Institut de Recherche Mathématique de Rennes

We prove that if $\Gamma$ is a lattice in a classical simple Lie group $G$, then the symmetric space of $G$ is $\Gamma$-equivariantly homotopy equivalent to a proper cocompact $\Gamma$-CW complex of dimension the virtual cohomological dimension of $\Gamma$.

Domaines: Topologie algébrique [math.AT]; Théorie des groupes [math.GR]

Javier Aramayona, Dieter Degrijse, Conchita Martinez-Perez, Juan Souto. Geometric dimension of lattices in classical simple Lie groups. Journal of topology, 2017, 10 (2), pp.632-667. ⟨10.1112/topo.12016⟩. ⟨hal-01145036⟩