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Von Neumann Betti numbers and Novikov type inequalities


Author: Michael Farber
Journal: Proc. Amer. Math. Soc. 128 (2000), 2819-2827
MSC (1991): Primary 58Exx; Secondary 57R19
DOI: https://doi.org/10.1090/S0002-9939-00-05340-5
Published electronically: February 29, 2000
MathSciNet review: 1664370
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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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Additional Information

Michael Farber
Affiliation: School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv 69978, Israel
Email: farber@math.tau.ac.il

DOI: https://doi.org/10.1090/S0002-9939-00-05340-5
Received by editor(s): October 19, 1998
Published electronically: February 29, 2000
Additional Notes: This research was partially supported by the US - Israel Binational Science Foundation, by the Herman Minkowski Center for Geometry, and by EPSRC grant GR/M20563.
Communicated by: Jozef Dodziuk
Article copyright: © Copyright 2000 American Mathematical Society

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