2007/06/26 by Clara Loeh, Roman Sauer, Loeh, Clara +1
Mathematics · #53C23 #53C35 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.DG #math.GT #msc:53C23 #msc:53C35
paper · pdf · doi:10.48550/arxiv.0706.3904
11 pages; rearrangement of section and minor changes; final version; to appear in Commentarii Mathematici Helvetici
openalex publication_date 2007/06/26 · arxiv created 2007/11/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The simplicial volume introduced by Gromov provides a topologically accessible lower bound for the minimal volume. Lafont and Schmidt proved that the simplicial volume of closed, locally symmetric spaces of non-compact type is positive. In this paper, we present a generalization of this result to certain non-compact locally symmetric spaces of finite volume, to so-called Hilbert modular varieties. The key idea is to reduce the problem to the compact case by first relating the simplicial volume of these manifolds to the Lipschitz simplicial volume and then taking advantage of a proportionality principle for the Lipschitz simplicial volume. Moreover, using computations of Bucher-Karlsson for the simplicial volume of products of closed surfaces, we obtain the exact value of the simplicial volume of Hilbert modular surfaces.