Reducible And Finite Dehn Fillings

TL;DR

This paper proves that in hyperbolic knot manifolds, the distance between finite and reducible filling slopes on the boundary is at most one, providing a bound on how these slopes relate.

Contribution

It establishes a new upper bound of one on the distance between finite and reducible filling slopes in hyperbolic knot manifolds.

Findings

Distance between finite and reducible slopes is at most one

Provides constraints on Dehn fillings in hyperbolic knot manifolds

Advances understanding of the relationship between different types of fillings

Abstract

We show that the distance between a finite filling slope and a reducible filling slope on the boundary of a hyperbolic knot manifold is at most one.