The Dijkgraaf-Witten invariant is a partial case of the photography method

TL;DR

This paper demonstrates that the Dijkgraaf-Witten invariants of manifolds are a specific instance of the more general photography principle, which is a versatile method for solving equations and constructing manifold invariants.

Contribution

It shows that the Dijkgraaf-Witten invariants can be interpreted as an example of the photography principle, highlighting the principle's broad applicability.

Findings

Dijkgraaf-Witten invariants fit into the photography principle framework

The photography principle generalizes methods for solving equations and constructing invariants

The paper provides a conceptual link between two approaches in topology

Abstract

In \cite{ManturovNikonovMay2023,ManturovWanMay2023} the author discovered a very general principle (called {\em the photography principle}) which allows one: a) To solve various equations (like pentagon equation) b) To construct invariants of manifolds. The advantage of that principle is that it deals with a very general notion of {\em data} and {\em data transmission} which may be of any kind. In the present paper, we show that the definition of the Dijkgraaf-Witten invariants of manifolds can be thought of as an evidence of the above principle.