2021/10/17 by Igor G. Korepanov, Korepanov, Igor G.
Mathematics · Physics and Astronomy · #15A24 #57K16 (Primary) #57Q99 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #math-ph #math.CO #math.MP #math.QA #msc:15A24 #msc:57K16 #msc:57Q99
paper · pdf · doi:10.48550/arxiv.2110.08780
15 pages, 2 figures
arxiv created 2021/10/17 · arxiv updated 2021/10/19
A cohomology theory is proposed for the recently discovered heptagon relation -- an algebraic imitation of a 5-dimensional Pachner move 4--3. 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.