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 | References | Similar Articles | Additional Information

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 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