A census of exceptional Dehn fillings

TL;DR

This paper provides a comprehensive catalog of all exceptional Dehn fillings on certain hyperbolic 3-manifolds, supporting existing conjectures and proposing new ones based on extensive data analysis.

Contribution

It offers the first complete enumeration of exceptional Dehn fillings for manifolds with up to 9 ideal tetrahedra, advancing understanding in 3-manifold topology.

Findings

Data supports standard conjectures about Dehn filling

Identifies 205,822 exceptional fillings

Suggests new conjectures based on data

Abstract

This paper describes the complete list of all 205,822 exceptional Dehn fillings on the 1-cusped hyperbolic 3-manifolds that have ideal triangulations with at most 9 ideal tetrahedra. The data is consistent with the standard conjectures about Dehn filling and suggests some new ones.