Examples of reducible and finite Dehn fillings

TL;DR

This paper constructs examples of hyperbolic 3-manifolds with reducible and finite Dehn fillings of all types, expanding understanding of their possible configurations.

Contribution

It provides the first examples of hyperbolic manifolds with reducible and finite Dehn fillings of every finite type, illustrating the diversity of such fillings.

Findings

Examples of hyperbolic manifolds with all types of finite Dehn fillings

Demonstrates the coexistence of reducible and finite fillings of various types

Expands the known landscape of Dehn filling configurations

Abstract

If a hyperbolic 3-manifold M admits a reducible and a finite Dehn filling, the distance between the filling slopes is known to be 1. This has been proved recently by Boyer, Gordon and Zhang. The first example of a manifold with two such fillings was given by Boyer and Zhang. In this paper, we give examples of hyperbolic manifolds admitting a reducible Dehn filling and a finite Dehn filling of every type: cyclic, dihedral, tetrahedral, octahedral and icosahedral.