English

Growth of Betti Numbers

Geometric Topology 2007-05-23 v1 Differential Geometry

Abstract

Suppose X is any finite complex with vanishing L^2 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.

Keywords

Cite

@article{arxiv.math/0111120,
  title  = {Growth of Betti Numbers},
  author = {Bryan Clair and Kevin Whyte},
  journal= {arXiv preprint arXiv:math/0111120},
  year   = {2007}
}

Comments

22 pages

R2 v1 2026-07-22T16:41:31.269Z