Platonic polyhedra tune the 3-sphere: III. Harmonic analysis on octahedral spherical 3-manifolds

摘要

From the homotopy groups of three distinct octahedral spherical 3-manifoldswe construct the isomorphic groups H of deck transformations acting on the3-sphere. The H-invariant polynomials on the 3-sphere constructed byrepresentation theory span the bases for the harmonic analysis on threespherical manifolds. Analysis of the Cosmic Microwave Background in terms ofthese new bases can reveal a non-simple topology of the space part ofspace-time.