A handlebody calculus for topology change

TL;DR

This paper explores topology-changing processes in quantum gravity using Morse theory and handlebodies, showing that certain higher-dimensional object nucleations are possible transitions with non-zero amplitude.

Contribution

It introduces a handlebody calculus framework to characterize topology change in quantum gravity, extending previous approaches with new mathematical tools.

Findings

Topology change processes are characterized using Morse theory.

Certain higher-dimensional objects can nucleate with non-zero amplitude.

The framework supports the possibility of topology change in quantum gravity.

Abstract

We consider certain interesting processes in quantum gravity which involve a change of spatial topology. We use Morse theory and the machinery of handlebodies to characterise topology changes as suggested by Sorkin. Our results support the view that that the pair production of Kaluza-Klein monopoles and the nucleation of various higher dimensional objects are allowed transitions with non-zero amplitude.