The fundamental group of a spherical space form is not audible

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Mauro Colantonio, Emilio A. Lauret
DOI: 10.48550/arxiv.2602.12939
Cited by: 0

Abstract

We revisit the problem of isospectral spherical space forms with non-cyclic fundamental groups after the works by Ikeda, Gilkey and Wolf. We find the first pair of spherical space forms with non-isomorphic fundamental groups and the same Laplace spectrum. This shows that the isomorphism class of the fundamental group is not audible among spherical space forms. We also found several instances where one can hear the fundamental group of a spherical space form (among spherical space forms).

Fields of Study & Subjects

Spectral Theory in Mathematical Physics Advanced Algebra and Geometry Geometric and Algebraic Topology

Publication details

Journal / source
arXiv (Cornell University)
Publication date
13 February 2026
Language
EN
Document type
Preprint