Surface subgroups for lattices in Fuchsian buildings

2014/07/15 by David Constantine, Jean‐François Lafont, Constantine, David +4 · 3 citations
Mathematics · #20F67 #57M07 #57M20 #Advanced Algebra and Geometry #Algebra over a field #FOS: Mathematics #Fuchsian group #Geometric and Algebraic Topology #Geometry #Geometry and complex manifolds #Group (periodic table) #Group Theory (math.GR) #Lattice (music) #Mathematical analysis #Mathematics #Physics #Piecewise #Pure mathematics #Quantum mechanics #Quotient #Surface (topology) #math.GR #msc:20F67 #msc:57M07 #msc:57M20

paper · pdf · doi:10.48550/arxiv.1407.3958

published in arXiv (Cornell University) (Cornell University) · This paper has been withdrawn by the authors due to an error in the proof of Fact 3

openalex publication_date 2014/07/15 · arxiv created 2014/09/03 · arxiv updated 2014/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Orbihedra of nonpositive curvature
• On L2-cohomology and Property (T) for Automorphism Groups of Polyhedral Cell Complexes
• Metric Spaces of Non-Positive Curvature
• Immersing almost geodesic surfaces in a closed hyperbolic three manifold
• Incompressible surfaces in rank one locally symmetric spaces

Related

• Surface Quotients of Right-Angled Hyperbolic Buildings
• Surface subgroups on 1-vertex and 3-vertex polyhedra forming triangular hyperbolic buildings
• Groups acting on CAT(0) square complexes
• ℂ-Fuchsian subgroups of some non-arithmetic lattices
• Invariant subspaces for some surface groups acting on A2-Euclidean buildings