Growth of Betti Numbers

Details Growth of Betti Numbers Growth of Betti Numbers

2001-11-09

arxiv.org/abs/math/0111120v1

Mathematics

Geometric Topology

22 pages

Scientific paper

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.

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