Building blocks for topology change in 3D

TL;DR

This paper classifies elementary topology changes in 3D manifolds using Morse theory, providing a set of fundamental cobordisms with physical interpretations relevant to quantum gravity.

Contribution

It identifies and characterizes the elementary cobordisms for 3D topology change, linking mathematical structures to physical phenomena in quantum gravity.

Findings

Classified three elementary cobordisms in 3D topology.

Connected topology changes to physical processes like wormholes and Big Bang.

Provided a framework for sum over topologies in quantum gravity.

Abstract

We investigate topology change in 3D. Using Morse theory and handle decomposition we find the set of elementary cobordisms for 3-manifolds. These are: (i) \O <-> S^2; (ii) \Sigma_g <-> \Sigma_{g+1}; (iii) \Sigma_{g_1} \sqcup \Sigma_{g_2} <-> \Sigma_{g_1+g_2} and they have appealing physical interpretations, e.g. Big Bang/Big Crunch, wormhole creation/annihilation and Einstein-Rosen bridge creation/annihilation, respectively. This decomposition into building blocks can be used in the path integral approach to quantum gravity in the sum over topologies.