Heptagon relations from a simplicial 3-cocycle, and their cohomology

Abstract

We introduce new algebraic structures associated with heptagon relations -- higher analogue of the well-known pentagon. The main points we deal with are: (i) polygon relations as algebraic imitations of Pachner moves, on the example of heptagon, (ii) parameterization of heptagon relations by simplicial 3-cocycles, (iii) applications to invariants of pairs "piecewise linear 5-manifold, a 3rd cohomology class on it".

20 pages. v4: sections 9 and 10 made, hopefully, more elegant and understandable

References in corpus (4)

• Simplex and Polygon Equations
• Hexagon cohomologies and polynomial TQFT actions
• Pentagon Relations in Direct Sums and Grassmann Algebras
• Odd-gon relations and their cohomology