A formula with hypervolumes of six 4-simplices and two discrete curvatures
I. G. Korepanov
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.
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