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.

arXiv comment23 pages, 3 figures

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Cited by in corpus (38)

• Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology
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• Growing a `Cosmic Beast': Observations and Simulations of MACS J0717.5+3745
• The decategorification of sutured Floer homology
• A note on cabling and L-space surgeries
• Characterizing slopes for torus knots
• Connected sums and involutive knot Floer homology
• Surgery obstructions from Khovanov homology
• Instanton Floer homology, sutures, and Heegaard diagrams
• Dehn surgery, rational open books and knot Floer homology
• On concordances in 3-manifolds
• Finite Dehn surgeries on knots in $S^3$
• Rational cobordisms and integral homology
• The lens space realization problem
• Strong Heegaard diagrams and strong L-spaces
• Homological actions on sutured Floer homology
• Instanton Floer homology, sutures, and Euler characteristics
• A complete list of lens spaces constructed by Dehn surgery I
• Does Khovanov homology detect the unknot?
• Knot Complement Problem for L-space $\mathbb{Z}H{S}^3$
• Null surgery on knots in L-spaces
• SU(2) representations and a large surgery formula
• Non-simple genus minimizers in lens spaces
• Heegaard Floer correction terms and rational genus bounds
• Homology spheres yielding lens spaces
• The Poincare homology sphere and almost simple knots in lens spaces
• Tunnel number one knots satisfy the Berge Conjecture
• H(2)-Unknotting Operation Related to 2-Bridge Links
• Rational Seifert Surfaces in Seifert Fibered Spaces
• Invariants for Legendrian knots in lens spaces
• Studies of distance one surgeries on the lens space $L(p,1)$
• A note on Grid Homology in lens spaces: $\mathbb{Z}$ coefficients and computations
• On manifolds with multiple lens space filings
• A Cabling Conjecture for Knots in Lens Spaces
• Distance one surgeries on the lens space $L(n,1)$
• Some applications of Gabai's internal hierarchy
• Knots which admit a surgery with simple knot Floer homology groups
• On Legendrian surgeries between lens spaces