Growth of Betti Numbers

2001/11/09 by Bryan Clair, Clair, Bryan, Kevin Whyte +1
Computer Science · Mathematics · #57M10 #Advanced Combinatorial Mathematics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Topological and Geometric Data Analysis #math.DG #math.GT #msc:57M10

paper · pdf · doi:10.48550/arxiv.math/0111120

22 pages

arxiv created 2001/11/09 · openalex publication_date 2001/11/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose X is any finite complex with vanishing L² Betti number. We prove upper bounds on the Betti numbers for regular coverings of X, sublinear in the order of covering. The bounds are sensitive to the Novikov-Shubin invariants of X, and are improved in the presence of a spectral gap.

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