The classification of exceptional Dehn surgeries on 2-bridge knots

TL;DR

This paper classifies all exceptional Dehn surgeries on 2-bridge knots, identifying when they yield reducible, toroidal, or small Seifert fibered manifolds, thus advancing understanding of 3-manifold topology.

Contribution

It provides a complete classification of exceptional Dehn surgeries on 2-bridge knots, detailing the resulting manifold types and expanding existing topological knowledge.

Findings

Identifies all surgeries producing reducible manifolds

Classifies surgeries resulting in toroidal manifolds

Determines surgeries leading to small Seifert fibered spaces

Abstract

We will classify all exceptional Dehn surgeries on 2-bridge knots according to whether they produce reducible, toroidal, or small Seifert fibered manifolds.