On the zero-in-the-spectrum conjecture


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 $\tilde M$.

DOI: 10.2307/3062113


Michael Farber

Shmuel Weinberger