Cyclic and finite surgeries on Montesinos knots

TL;DR

This paper classifies all Dehn surgeries on Montesinos knots that produce manifolds with cyclic or finite fundamental groups, providing a comprehensive understanding of these special surgeries.

Contribution

It offers a complete classification of cyclic and finite surgeries on Montesinos knots, filling a gap in the understanding of their fundamental group properties.

Findings

Identifies all surgeries resulting in cyclic fundamental groups

Identifies all surgeries resulting in finite fundamental groups

Provides a complete classification for Montesinos knots

Abstract

We give a complete classification of the Dehn surgeries on Montesinos knots which yield manifolds with cyclic or finite fundamental groups.