A formula with hypervolumes of six 4-simplices and two discrete curvatures
Exactly Solvable and Integrable Systems
2007-05-23 v1 General Relativity and Quantum Cosmology
High Energy Physics - Lattice
Metric Geometry
Quantum Algebra
Abstract
One of the generalizations of the pentagon equation to higher dimensions is the so-called "six-term equation". Geometrically, it corresponds to one of the "Alexander moves", that is elementary rebuildings of simplicial complexes, namely, replacing a "cluster" of three 4-simplices by another "cluster", also of three 4-simplices and with the same boundary. We present a formula containing the euclidean volumes of the simplices in the first cluster in its l.h.s., and those in the second cluster - in its r.h.s. The formula also involves "discrete curvatures" appearing when we slightly deform the euclidean space.
Keywords
Cite
@article{arxiv.nlin/0003024,
title = {A formula with hypervolumes of six 4-simplices and two discrete curvatures},
author = {I. G. Korepanov},
journal= {arXiv preprint arXiv:nlin/0003024},
year = {2007}
}
Comments
LaTeX, 3 pages, continues solv-int/9911008 and nlin.SI/0003001