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Exact Polynomial Eigenmodes for Homogeneous Spherical 3-Manifolds

Jeffrey R. Weeks
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Abstract

Observational data hints at a finite universe, with spherical manifolds such as the Poincare dodecahedral space tentatively providing the best fit. Simulating the physics of a model universe requires knowing the eigenmodes of the Laplace operator on the space. The present article provides explicit polynomial eigenmodes for all globally homogeneous 3-manifolds: the Poincare dodecahedral space S3/I*, the binary octahedral space S3/O*, the binary tetrahedral space S3/T*, the prism manifolds S3/D_m* and the lens spaces L(p,1).

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Jeffrey R. Weeks. 2006-10-25. Exact Polynomial Eigenmodes for Homogeneous Spherical 3-Manifolds. https://doi.org/10.1088/0264-9381%2F23%2F23%2F023

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