Von Neumann Betti numbers and Novikov type inequalities
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- by Michael Farber PDF
- 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.References
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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
- 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
- © Copyright 2000 American Mathematical Society
- 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
- MathSciNet review: 1664370