Hyperbolic knots with three toroidal Dehn surgeries

TL;DR

This paper demonstrates that infinitely many hyperbolic knots can have exactly three toroidal Dehn surgeries, supporting the conjecture that such knots admit at most three such surgeries, with these surgeries occurring at consecutive integers.

Contribution

The authors construct infinitely many hyperbolic knots with exactly three toroidal Dehn surgeries at consecutive integers, providing evidence for the conjectured maximum.

Findings

Existence of infinitely many hyperbolic knots with three toroidal surgeries

Surgeries occur at consecutive integer slopes

Supports the conjecture on the maximum number of such surgeries

Abstract

It is conjectured that a hyperbolic knot admits at most three Dehn surgeries which yield closed three manifolds containing incompressible tori. We show that there exist infinitely many hyperbolic knots which attain the conjectural maximum number. Interestingly, those surgeries correspond to consecutive integers.