Two-cocycles give a full nonlinear parameterization of the simplest 3--3 relation
Abstract
A parameterization of Grassmann-algebraic relations corresponding to the Pachner move 3--3 is proposed. In these relations, each 4-simplex is assigned a Grassmann weight depending on five anticommuting variables associated with its 3-faces. The weights are chosen to have the "simplest" form - a Grassmann--Gaussian exponent or its analogue (satisfying a similar system of differential equations). Our parameterization works for a Zariski open set of such relations, looks relevant from the algebraic-topological viewpoint, and reveals intriguing nonlinear relations between objects associated with simplices of different dimensions.
Cite
@article{arxiv.1310.4075,
title = {Two-cocycles give a full nonlinear parameterization of the simplest 3--3 relation},
author = {Igor G. Korepanov},
journal= {arXiv preprint arXiv:1310.4075},
year = {2017}
}
Comments
25 pages. v3: the accepted version. The final publication is available at link.springer.com, see journal-ref and DOI here