Properties of 3-manifolds for relativists

TL;DR

This paper reviews key topological properties of 3-manifolds relevant to relativists, focusing on diffeomorphism groups and summarizing recent and classical results in the context of quantum gravity.

Contribution

It provides a comprehensive summary of the topological features of 3-manifolds, including new insights into their diffeomorphism groups, relevant for canonical quantum gravity.

Findings

Summary of topological properties of 3-manifolds

New results on diffeomorphism groups

Discussion of large diffeomorphisms in specific 3-manifolds

Abstract

In canonical quantum gravity certain topological properties of 3-manifolds are of interest. This article gives an account of those properties which have so far received sufficient attention, especially those concerning the diffeomorphism groups of 3-manifolds. We give a summary of these properties and list some old and new results concerning them. The appendix contains a discussion of the group of large diffeomorphisms of the $l$-handle 3-manifold.