On the zero-in-the-spectrum conjecture

1999/11/11 by Michael Färber, M. Farber, Shmuel Weinberger +3
Mathematics · #57Q10 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.DG #math.SP #msc:57Q10

paper · pdf · doi:10.48550/arxiv.math/9911077

13 pages

arxiv created 1999/11/11 · openalex publication_date 1999/11/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 L² forms of all degrees on the universal covering of M.

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