Platonic polyhedra tune the 3-sphere: II. Harmonic analysis on cubic spherical 3-manifolds

Details Platonic polyhedra tune the 3-sphere: II. Harmonic analysis on cubic spherical 3-manifolds Platonic polyhedra tune the 3-sphere: II. Harmonic analysis on cubic spherical 3-manifolds

2009-01-05

arxiv.org/abs/0901.0511v4

Phys.Scripta 80:025902,2009

Mathematics

Differential Geometry

19 pages, 3 figures, expression for basis polynomials given, comparison with related publications

Scientific paper

10.1088/0031-8949/80/02/025902

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.

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