Algebraic relations with anticommuting variables for four-dimensional Pachner moves 3 -> 3 and 2 <-> 4

TL;DR

The paper introduces algebraic relations using Grassmann variables and Berezin integrals for Pachner moves 3 -> 3 and 2 <-> 4, forming part of a 4D topological quantum field theory framework.

Contribution

It presents simple algebraic relations in Grassmann variables for key Pachner moves, advancing the algebraic foundation of 4D topological quantum field theories.

Findings

Relations correspond to Pachner moves 3 -> 3 and 2 <-> 4

Relations are expressed via Grassmann anticommuting variables

Provides two thirds of the algebraic foundation for 4D TQFT

Abstract

Relatively simple algebraic relations are presented corresponding to Pachner moves 3 -> 3 and 2 <-> 4, thus providing two thirds of the foundation for a four-dimensional topological quantum field theory. These relations are written in terms of Grassmann anticommuting variables and Berezin integral.