Invariants of Braided Ribbon Networks

TL;DR

This paper introduces a unified framework for braided ribbon networks in 3D manifolds, defines evolution moves dual to Pachner moves, and presents an invariant that connects to prior research.

Contribution

It provides a consistent definition for braided ribbon networks, unifies different valences, and introduces an invariant linked to network evolution and Pachner moves.

Findings

Unified framework for 3D braided ribbon networks

Defined evolution moves dual to Pachner moves

Presented an invariant of network evolution

Abstract

We present a consistent definition for braided ribbon networks in 3-dimensional manifolds, unifying both three and four valent networks in a single framework. We present evolution moves for these networks which are dual to the Pachner moves on simplices and present an invariant of this evolution. Finally we relate these results back to previous work in the subject.