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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



An algorithmically unsolvable problem in analysis

Authors: A. Lenard and J. Stillwell
Journal: Proc. Amer. Math. Soc. 88 (1983), 129-130
MSC: Primary 58G25; Secondary 03D35
MathSciNet review: 691292
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Abstract: The decision problem of distinguishing between the cases when the Laplace-Beltrami operator on the covering space of a compact manifold has 0 in its spectrum or is bounded away from 0 is algorithmically unsolvable in any class of manifolds that includes all $ 4$-dimensional ones. The proof depends on a result of Brooks connecting the spectrum with the amenability of the fundamental group.

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Keywords: Unsolvability, Laplacian on manifolds, spectrum on Laplacian, amenability, Markov property
Article copyright: © Copyright 1983 American Mathematical Society

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