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

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.