Platonic polyhedra tune the 3-sphere: II. Harmonic analysis on cubic spherical 3-manifolds
arXiv:0901.0511 · doi:10.1088/0031-8949/80/02/025902
Abstract
From the homotopy groups of two cubic spherical 3-manifolds we construct the isomorphic groups of deck transformations acting on the 3-sphere. These groups become the cyclic group of order eight and the quaternion group respectively. By reduction of representations from the orthogonal group to the identity representation of these subgroups we provide two subgroup-periodic bases for the harmonic analysis on the 3-manifolds. This harmonic analysis has applications to cosmic topology.
19 pages, 3 figures, expression for basis polynomials given, comparison with related publications