Platonic polyhedra tune the 3-sphere: III. Harmonic analysis on octahedral spherical 3-manifolds
Mathematical Physics
2010-04-26 v2 math.MP
Abstract
From the homotopy groups of three distinct octahedral spherical 3-manifolds we construct the isomorphic groups H of deck transformations acting on the 3-sphere. The H-invariant polynomials on the 3-sphere constructed by representation theory span the bases for the harmonic analysis on three spherical manifolds. Analysis of the Cosmic Microwave Background in terms of these new bases can reveal a non-simple topology of the space part of space-time.
Keywords
Cite
@article{arxiv.0908.1000,
title = {Platonic polyhedra tune the 3-sphere: III. Harmonic analysis on octahedral spherical 3-manifolds},
author = {Peter Kramer},
journal= {arXiv preprint arXiv:0908.1000},
year = {2010}
}
Comments
12 pages, 1 figure