Platonic polyhedra tune the three-sphere: II. Harmonic analysis on cubic spherical manifolds
نویسندگان
چکیده
منابع مشابه
Platonic polyhedra tune the 3 - sphere : II . Harmonic analysis on cubic spherical 3 - manifolds
From the homotopy groups of two cubic spherical 3-manifolds we construct the iso-morphic 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 harmoni...
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We view a spherical topological 3-manifold M, see [11] and [13], as a prototile on its cover M̃ = S. We studied in [7] the isometric actions of O(4, R) on the 3sphere S and gave its basis as well-known homogeneous Wigner polynomials in [5] eq.(37). An algorithm due to Everitt in [3] generates the homotopies for all spherical 3-manifolds M from five Platonic polyhedra. Using intermediate Coxeter ...
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A spherical topological manifold of dimension n − 1 forms a prototile on its cover, the (n-1)-sphere. The tiling is generated by the fixpoint-free action of the group of deck transformations. By a general theorem, this group is isomorphic to the first homotopy group. Multiplicity and selection rules appear in the form of reduction of group representations. A basis for the harmonic analysis on t...
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A spherical topological manifold of dimension n − 1 forms a prototile on its cover, the (n-1)-sphere. The tiling is generated by the fixpoint-free action of the group of deck transformations. By a general theorem, this group is isomorphic to the first homotopy group. Multiplicity and selection rules appear in the form of reduction of group representations. A basis for the harmonic analysis on t...
متن کاملTopology of Platonic Spherical Manifolds: From Homotopy to Harmonic Analysis
We carry out the harmonic analysis on four Platonic spherical three-manifolds with different topologies. Starting out from the homotopies (Everitt 2004), we convert them into deck operations, acting on the simply connected three-sphere as the cover, and obtain the corresponding variety of deck groups. For each topology, the three-sphere is tiled into copies of a fundamental domain under the cor...
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ژورنال
عنوان ژورنال: Physica Scripta
سال: 2010
ISSN: 0031-8949,1402-4896
DOI: 10.1088/1402-4896/82/1/019802