Lens space surgeries and L-space homology spheres

TL;DR

This paper establishes criteria for when knots in L-spaces can be surgered to produce L-space homology spheres, and applies these to reformulate Berge's conjecture on lens space surgeries in S^3.

Contribution

It provides necessary and sufficient conditions for L-space surgeries on knots and reformulates a longstanding conjecture in the field.

Findings

Criteria for L-space homology sphere surgeries on knots

Reformulation of Berge's conjecture on lens space surgeries

Enhanced understanding of knot surgeries in L-spaces

Abstract

We describe necessary and sufficient conditions for a knot in an L-space to have an L-space homology sphere surgery. We use these conditions to reformulate a conjecture of Berge about which knots in S^3 admit lens space surgeries.