Von Neumann Betti numbers and Novikov type inequalities

Michael Farber

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arXiv · math/9810114

Von Neumann Betti numbers and Novikov type inequalities

Michael Farber

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Abstract

It is shown that the Novikov inequalities for critical points of closed 1-forms hold with the von Neumann Betti numbers replacing the Novikov numbers. As a corollary we obtain a vanishing theorem for $L^2$ cohomology, generalizing a theorem of W. Lueck. We also prove that von Neumann Betti numbers coincide with the Novikov numbers for free abelian coverings.

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BibTeX RIS

Michael Farber. 1998-10-18. Von Neumann Betti numbers and Novikov type inequalities. https://arxiv.org/abs/math/9810114

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