Finiteness Properties of Non-Uniform Lattices on CAT(0) Polyhedral Complexes

2011/08/01 by Giovanni Gandini, Gandini, Giovanni, G Gandini
Computer Science · Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #math.GR

paper · pdf · doi:10.48550/arxiv.1108.0252

arxiv created 2011/08/01 · openalex publication_date 2011/08/01 · arxiv updated 2011/08/02 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We show that the homological finiteness length of a non-uniform lattice on a locally finite CAT(0) n-dimensional polyhedral complex is less than n. As a corollary, we obtain an upper bound for the homological finiteness length of arithmetic groups over function fields. This gives an easier proof of a result of Bux and Wortman that solved a long-standing conjecture.

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