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On the zero-in-the-spectrum conjecture

M. Farber·S. Weinberger
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Abstract

We prove that the answer to the "zero-in-the-spectrum" conjecture, in its form, suggested by J. Lott, is negative. Namely, we show that for any n > 5 there exists a closed n-dimensional manifold M, 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 of M.

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M. Farber, S. Weinberger. 1999-11-11. On the zero-in-the-spectrum conjecture. https://arxiv.org/abs/math/9911077

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