The Fundamental Group of a Spatial Section Represented by a Topspin Network

TL;DR

This paper introduces an algorithm using topspin networks to determine the fundamental group of spatial sections, enabling topology tracking and demonstrating spatial topology change in smooth 4-manifolds.

Contribution

The paper presents a novel algorithm that leverages topspin networks to analyze spatial topology, a capability absent in standard Loop Quantum Gravity.

Findings

Successfully determines the fundamental group of spatial sections.

Enables tracking of topology changes in quantum gravity models.

Provides an example of spatial topology change in a smooth 4-manifold.

Abstract

We present an algorithm which determines the fundamental group of a spatial section using topspin networks. Tracking the topology of the spatial section is a unique feature of this approach, which is not possible in standard Loop Quantum Gravity. This leads to an example of spatial topology change in a smooth 4-manifold represented by a topspin foam.