Exact Polynomial Eigenmodes for Homogeneous Spherical 3-Manifolds
Spectral Theory
2009-11-11 v3 Astrophysics
Geometric Topology
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).
Cite
@article{arxiv.math/0502566,
title = {Exact Polynomial Eigenmodes for Homogeneous Spherical 3-Manifolds},
author = {Jeffrey R. Weeks},
journal= {arXiv preprint arXiv:math/0502566},
year = {2009}
}
Comments
v3. Final published version. 27 pages, 1 figure