Lens spaces obtainable by surgery on doubly primitive knots

TL;DR

This paper provides an algorithm to determine which lens spaces can be obtained by Dehn surgery on doubly primitive knots, offering a complete classification including cases with Klein bottles.

Contribution

It introduces a decision algorithm and characterizes all lens spaces obtainable through such surgeries, including those with Klein bottles.

Findings

Algorithm to decide lens space obtainability

Complete classification of lens spaces from doubly primitive knots

Characterization of surgeries yielding lens spaces with Klein bottles

Abstract

In this paper, we consider which lens spaces are obtainable by Dehn surgery described by Berge on doubly primitive knots. It is given an algorithm to decide whether a given lens space is obtainable by such surgery. Also included is a complete characterization of such surgery yielding lens spaces with Klein bottles.