Quadratic heptagon cohomology
Abstract
A cohomology theory is proposed for the recently discovered heptagon relation  an algebraic imitation of a 5dimensional Pachner move 43. In particular, `quadratic cohomology' is introduced, and it is shown that it is quite nontrivial, and even more so if compare heptagon with either its higher analogues, such as enneagon or hendecagon, or its lower analogue, pentagon. Explicit expressions for the nontrivial quadratic heptagon cocycles are found in dimensions 4 and 5.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 DOI:
 10.48550/arXiv.2110.08780
 arXiv:
 arXiv:2110.08780
 Bibcode:
 2021arXiv211008780K
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematical Physics;
 Mathematics  Combinatorics;
 15A24;
 57K16 (Primary);
 57Q99 (Secondary)
 EPrint:
 15 pages, 2 figures