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On the zero-in-the-spectrum conjecture

Farber, M.; Weinberger, S.

Authors

M. Farber

S. Weinberger



Abstract

We prove that the answer to the "zero-in-the-spectrum" conjecture, in the form suggested by J. Lott, is negative. Namely, we show that for any $n\ge 6$ there exists a closed $n$-dimensional smooth manifold $M^n$, so that zero does not belong to the spectrum of the Laplace-Beltrami operator acting on the $L^2$ forms of all degrees on the universal covering $\tilde M$.

Citation

Farber, M., & Weinberger, S. (2001). On the zero-in-the-spectrum conjecture. Annals of Mathematics, 154(1), 139 - 154. https://doi.org/10.2307/3062113

Journal Article Type Article
Publication Date 2001-07
Deposit Date May 1, 2007
Journal Annals of Mathematics
Print ISSN 0003-486X
Publisher Department of Mathematics
Peer Reviewed Peer Reviewed
Volume 154
Issue 1
Pages 139 - 154
DOI https://doi.org/10.2307/3062113
Publisher URL http://annals.math.princeton.edu/issues/2001/154_1.html

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