Lens space surgeries and L-space homology spheres

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.

23 pages, 3 figures

References in corpus (6)

• Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology
• Monopoles and lens space surgeries
• Small genus knots in lens spaces have small bridge number
• On Floer homology and the Berge conjecture on knots admitting lens space surgeries
• On the non-existence of L-space surgery structure
• Lens spaces given from L-space homology 3-spheres

Cited by in corpus (11)

• Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology
• The lens space realization problem
• Homological actions on sutured Floer homology
• A complete list of lens spaces constructed by Dehn surgery I
• Does Khovanov homology detect the unknot?
• SU(2) representations and a large surgery formula
• H(2)-Unknotting Operation Related to 2-Bridge Links
• Rational Seifert Surfaces in Seifert Fibered Spaces
• Invariants for Legendrian knots in lens spaces
• Knots which admit a surgery with simple knot Floer homology groups
• Distance one surgeries on the lens space $L(n,1)$