Growth of Betti Numbers

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.

22 pages

References in corpus (1)

• L2-determinant class and approximation of L2-Betti numbers

Cited by in corpus (2)

• d = 11 Supergravity on almost flat R^4 times a compact hyperbolic 7-manifold, and the dip and bump seen in ATLAS-CONF-2010-088
• Improvement of a provisional solution of the quantum-corrected field equations of d = 11 supergravity on flat R^4 times a compact hyperbolic 7-manifold, and modes that decay along the beam line outside the interaction region at the LHC