Observational data hint at a finite universe, with spherical manifolds such as the Poincaré 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 paper provides explicit polynomial eigenmodes for all globally homogeneous 3-manifolds: the Poincaré 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).
Classical and Quantum Gravity
- Pub Date:
- December 2006
- Mathematics - Spectral Theory;
- Mathematics - Geometric Topology;
- v3. Final published version. 27 pages, 1 figure