Orbifold construction of the modes of the Poincare dodecahedral space

Abstract

We provide a new construction of the modes of the Poincare dodecahedral space S^3/I*. The construction uses the Hopf map, Maxwell's multipole vectors and orbifolds. In particular, the *235-orbifold serves as a parameter space for the modes of S^3/I* shedding new light on the geometrical significance of the dimension of each space of $k$-modes, as well as on the modes themselves.

References in corpus (20)

• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• The axis of evil
• Cosmic Topology
• Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background
• Multipole Vectors--a new representation of the CMB sky and evidence for statistical anisotropy or non-Gaussianity at 2<=l<=8
• The optimal phase of the generalised Poincare dodecahedral space hypothesis implied by the spatial cross-correlation function of the WMAP sky maps
• Correlating anomalies of the microwave sky: The Good, the Evil and the Axis
• Polynomial Interpretation of Multipole Vectors
• Canonical representation of spherical functions: Sylvester's theorem, Maxwell's multipoles and Majorana's sphere
• A test of the Poincare dodecahedral space topology hypothesis with the WMAP CMB data
• CMB Alignment in Multi-Connected Universes
• A spatial correlation analysis for a toroidal universe
• The study of topology of the universe using multipole vectors
• Laplacian eigenmodes for spherical spaces
• Correlations between Maxwell's multipoles for gaussian random functions on the sphere
• Predicting the CMB power spectrum for binary polyhedral spaces
• Probability Density of the Multipole Vectors for a Gaussian Cosmic Microwave Background
• Constraining Cosmic Topology with CMB Polarization
• Exact Polynomial Eigenmodes for Homogeneous Spherical 3-Manifolds