Minimum-volume hyperbolic 3-manifolds

TL;DR

This paper completes the proof that the Weeks manifold is the smallest compact hyperbolic 3-manifold by enumerating small-volume manifolds obtained through Dehn filling, and identifies the ten smallest one-cusped hyperbolic 3-manifolds.

Contribution

It provides a complete enumeration of small-volume hyperbolic 3-manifolds derived from Mom-2 and Mom-3 manifolds, confirming the Weeks manifold's minimality.

Findings

Weeks manifold is the minimum-volume compact hyperbolic 3-manifold

Enumerates the 10 smallest one-cusped hyperbolic 3-manifolds

Completes the classification of small-volume hyperbolic 3-manifolds

Abstract

We enumerate the small-volume manifolds that can be obtained by Dehn filling on Mom-2 and Mom-3 manifolds as defined by Gabai, Meyerhoff, and the author. In so doing we complete the proof that the Weeks manifold is the minimum-volume compact hyperbolic 3-manifold, as well as enumerating the 10 smallest one-cusped hyperbolic 3-manifolds.