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# On the zero-in-the-spectrum conjecture.

Farber, M. and Weinberger, S. (2001) 'On the zero-in-the-spectrum conjecture.', Annals of mathematics., 154 (1). 139 - 154.

## 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 $\tilde M$.

Item Type: Article Full text not available from this repository. http://annals.math.princeton.edu/issues/2001/154_1.html 01 May 2007 08 Apr 2009 16:30

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