Nonconstant hexagon relations and their cohomology
Quantum Algebra
2021-01-07 v2 Algebraic Topology
Abstract
A construction of hexagon relations - algebraic realizations of four-dimensional Pachner moves - is proposed. It goes in terms of "permitted colorings" of 3-faces of pentachora (4-simplices), and its main feature is that the set of permitted colorings is nonconstant - varies from pentachoron to pentachoron. Further, a cohomology theory is formulated for these hexagon relations, and its nontriviality is demonstrated on explicit examples.
Cite
@article{arxiv.1812.10072,
title = {Nonconstant hexagon relations and their cohomology},
author = {Igor G. Korepanov},
journal= {arXiv preprint arXiv:1812.10072},
year = {2021}
}
Comments
26 pages; v2: improvements in Section 6, expression for 4-cocycle corrected