Growth of Betti Numbers
classification
🧮 math.GT
math.DG
keywords
bettiboundsnumberscomplexcoveringcoveringsfinitegrowth
read the original 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.
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