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2004 Tetra and Didi, the cosmic spectral twins
Peter G Doyle, Juan Pablo Rossetti
Geom. Topol. 8(3): 1227-1242 (2004). DOI: 10.2140/gt.2004.8.1227

Abstract

We introduce a pair of isospectral but non-isometric compact flat 3–manifolds called Tetra (a tetracosm) and Didi (a didicosm). The closed geodesics of Tetra and Didi are very different. Where Tetra has two quarter-twisting geodesics of the shortest length, Didi has four half-twisting geodesics. Nevertheless, these spaces are isospectral. This isospectrality can be proven directly by matching eigenfunctions having the same eigenvalue. However, the real interest of this pair – and what led us to discover it – is the way isospectrality emerges from the Selberg trace formula, as the result of a delicate interplay between the lengths and twists of closed geodesics.

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Peter G Doyle. Juan Pablo Rossetti. "Tetra and Didi, the cosmic spectral twins." Geom. Topol. 8 (3) 1227 - 1242, 2004. https://doi.org/10.2140/gt.2004.8.1227

Information

Received: 17 July 2003; Revised: 20 September 2004; Accepted: 21 September 2004; Published: 2004
First available in Project Euclid: 21 December 2017

zbMATH: 1091.58021
MathSciNet: MR2087082
Digital Object Identifier: 10.2140/gt.2004.8.1227

Subjects:
Primary: 57M50, 58J53
Secondary: 11F72, 53C22

Rights: Copyright © 2004 Mathematical Sciences Publishers

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