. M G ] 6 J un 1 99 9 Uniform partitions of 3 - space , their relatives and embedding ∗

J un 1 99 9 Uniform partitions of 3 - space , their relatives and embedding ∗

We review 28 uniform partitions of 3-space in order to find out which of them have graphs (skeletons) embeddable isometrically (or with scale 2) into some cubic lattice Zn. We also consider some relatives of those 28 partitions, including Achimedean 4-polytopes of Conway-Guy, non-compact uniform partitions, Kelvin partitions and those with unique vertex figure (i.e. Delaunay star). Among last o...

Uniform Partitions of 3-space, their Relatives and Embedding

We review 28 uniform partitions of 3-space in order to find out which of them have graphs (skeletons) embeddable isometrically (or with scale 2) into some cubic lattice Zn . We also consider some relatives of those 28 partitions, including Archimedean 4-polytopes of Conway–Guy, non-compact uniform partitions, Kelvin partitions and those with a unique vertex figure (i.e., Delaunay star). Among t...

ar X iv : d g - ga / 9 70 60 06 v 1 6 J un 1 99 7 ON THE HOMOTOPY INVARIANCE OF L 2 TORSION FOR COVERING SPACES

We prove the homotopy invariance of L torsion for covering spaces, whenever the covering transformation group is either residually finite or amenable. In the case when the covering transformation group is residually finite and when the L cohomology of the covering space vanishes, the homotopy invariance was established by Lück [Lu]. We also give some applications of our results.

ar X iv : d g - ga / 9 70 70 26 v 1 3 1 Ju l 1 99 7 COHERENT STATES , TRANSITION AMPLITUDES AND EMBEDDINGS

The transition amplitudes between coherent states on the coherent state manifold M are expressed in terms of the embedding of M into a projective Hilbert space PL. Consequences for the dimension of PL and a simple geometric interpretation of Calabi's diastasis follows. The coherent states [1] offer a powerful framework to formulate a link between classical and quantum mechanics [2, 3]. Simultan...

ar X iv : h ep - t h / 99 06 02 9 v 1 3 J un 1 99 9