Heptagon relations parameterized by simplicial 3-cocycles

TL;DR

This paper introduces a new family of algebraic relations called heptagon relations, which model five-dimensional Pachner moves and are parameterized by simplicial 3-cocycles, advancing the algebraic understanding of higher-dimensional topological transformations.

Contribution

It constructs a novel family of heptagon relations parameterized by simplicial 3-cocycles, linking algebraic structures with five-dimensional topological moves.

Findings

Heptagon relations successfully model 5D Pachner move 3-4.

Parameterization by simplicial 3-cocycles provides new algebraic tools.

Lays groundwork for algebraic topology in higher dimensions.

Abstract

We construct a family of heptagon relations -- algebraic imitations of five-dimensional Pachner move 3--4, parameterized by simplicial 3-cocycles.