On the zero-in-the-spectrum conjecture

• 成果类型: Article
• 署名作者: Farber, M; Weinberger, S
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/3062113
• 发表日期: 2001
• 页码: 139-154
• 关键词: asymptotic dimension; HOMOLOGY

摘要

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 greater than or equal to 6 there exists a closed n-dimensional smooth manifold A-P, 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 M.