43 citations · 152 across the 26 of their papers we have counts for
6 papers · 1 filter
Topology of Platonic Spherical Manifolds: From Homotopy to Harmonic Analysis
Peter Kramer
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…
Discrete Quantum Gravity: II. Simplicial complexes, irreps of SL(2,C), and a Lorentz invariant weight in a state sum model
P. Kramer, M. Lorente
In part I of [1] we have developed the tensor and spin representation of SO(4) in order to apply it to the simplicial decomposition of the Barrett-Crane model. We attach to each fa…
Harmonic polynomials for expanding the fluctuations of the Cosmic Microwave Background: The Poincare and the 3-sphere model
Peter Kramer
Fluctuations of the Cosmic Microwave Background CMB are observed by the WMAP. When expanded into the harmonic eigenmodes of the space part of a cosmological model, they provide ins…
Invariant operator due to F. Klein quantizes H. Poincare's dodecahedral 3-manifold
Peter Kramer
The eigenmodes of the Poincaré dodecahedral 3-manifold are constructed as eigenstates of a novel invariant operator. The topology of is characterized by the homotopy group…
Surface embedding, topology and dualization for spin networks
P. Kramer, M. Lorente
Spin networks are graphs derived from 3nj symbols of angular momentum. The surface embedding, the topology and dualization of these networks are considered. Embeddings into compact…
The double torus as a 2D cosmos: groups, geometry and closed geodesics
P. Kramer, M. Lorente
The double torus provides a relativistic model for a closed 2D cosmos with topology of genus 2 and constant negative curvature. Its unfolding into an octagon extends to an octagona…