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September 10, 2025

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

Key Points

Heptagon relations offer a higher analogue to pentagon relations, expanding algebraic frameworks significantly.
Invariants of pairs, including piecewise linear 5-manifolds, are characterized through new cohomology classes.
The study highlights polygon relations' role as algebraic imitations of Pachner moves, enhancing geometric understanding.
The parameterization of heptagon relations is advanced by utilizing simplicial 3-cocycles, enabling deeper algebraic exploration.

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 third cohomology class on it).

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Cite This Study

I. G. Korepanov (Fri,) studied this question.

synapsesocial.com/papers/68c1a78154b1d3bfb60e0f0f https://doi.org/https://doi.org/10.1063/5.0281756