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arXiv · 0908.1000

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

Peter Kramer
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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.

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Peter Kramer. 2009-10-13. Platonic polyhedra tune the 3-sphere: III. Harmonic analysis on octahedral spherical 3-manifolds. https://doi.org/10.1088/0031-8949%2F81%2F02%2F025005

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