Surface subgroups for lattices in Fuchsian buildings

Abstract

We consider finite 2-dimensional polyhedral complexes, equipped with piecewise non-positively curved, locally CAT(0) metrics. We give conditions on the complex X that ensure that its fundamental group contains a surface subgroup. Concrete examples covered by our methods include compact quotients of sufficiently thick Fuchsian buildings, where the lattice acts freely and the quotient has at least two vertices.

This paper has been withdrawn by the authors due to an error in the proof of Fact 3

References in corpus (1)

• Incompressible surfaces in rank one locally symmetric spaces

Cited by in corpus (2)

• Hyperbolic triangular buildings without periodic planes of genus two
• Surface subgroups on 1-vertex and 3-vertex polyhedra forming triangular hyperbolic buildings