Von Neumann Betti numbers and Novikov type inequalities

Farber, Michael

doi:10.1090/S0002-9939-00-05340-5

Von Neumann Betti numbers and Novikov type inequalities
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Proc. Amer. Math. Soc. 128 (2000), 2819-2827 Request permission

Abstract:

In this paper we show that Novikov type inequalities for closed 1-forms hold with the von Neumann Betti numbers replacing the Novikov numbers. As a consequence we obtain a vanishing theorem for $L^{2}$ cohomology. We also prove that von Neumann Betti numbers coincide with the Novikov numbers for free abelian coverings.

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