On realizations of Pachner moves in 4D

TL;DR

This paper analyzes the combinatorial structure of Pachner moves in 4D, focusing on the (3,3) move, and explores solutions related to Pontryagin self-dual groups, leading to models of 4D combinatorial TQFT.

Contribution

It characterizes solutions associated with Pontryagin self-dual groups and introduces a simple 4D combinatorial TQFT model based on finite abelian groups.

Findings

Solutions exhibit remarkable symmetry properties.

Finite abelian groups lead to a simple TQFT model.

Analysis of the (3,3) Pachner move in 4D.

Abstract

The combinatorial structure of Pachner moves in four dimensions is analyzed in the case of a distinguished move of the type (3,3) and few examples of solutions are reviewed. In particular, solutions associated to Pontryagin self-dual locally compact abelian groups are characterized with remarkable symmetry properties which, in the case of finite abelian groups, give rise to a simple model of combinatorial TQFT with corners in four dimensions.