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

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

2009-08-07

arxiv.org/abs/0908.1000v2

Phys. Scr. 81 025005 (2010)

Physics

Mathematical Physics

12 pages, 1 figure

Scientific paper

10.1088/0031-8949/81/02/025005

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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