2015/09/14 by Nicolas Tholozan, Tholozan, Nicolas · 2 citations
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1509.04178
openalex publication_date 2015/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Up to a finite cover, closed anti-de Sitter 3-manifolds are quotients of SO0(2,1) by a discrete subgroup of SO0(2,1) × SO0(2,1) of the form j× ρ(Γ)~, where Γ is the fundamental group of a closed oriented surface, j a Fuchsian representation and ρ another representation which is "strictly dominated" by j. Here we prove that the volume of such a quotient is proportional to the sum of the Euler classes of j and ρ. As a consequence, we obtain that this volume is constant under deformation of the anti-de Sitter structure. Our results extend to (not necessarily compact) quotients of SO0(n,1) by a discrete subgroup of SO0(n,1) × SO0(n,1).