Exact Polynomial Eigenmodes for Homogeneous Spherical 3-Manifolds

Details Exact Polynomial Eigenmodes for Homogeneous Spherical 3-Manifolds Exact Polynomial Eigenmodes for Homogeneous Spherical 3-Manifolds

2005-02-27

arxiv.org/abs/math/0502566v3

Class.Quant.Grav. 23 (2006) 6971-6988

Mathematics

Spectral Theory

v3. Final published version. 27 pages, 1 figure

Scientific paper

10.1088/0264-9381/23/23/023

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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