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