(1,1) L-space knots

Abstract

We characterize the (1, 1) knots in the three-sphere and lens spaces that admit non-trivial L-space surgeries. As a corollary, 1-bridge braids in these manifolds admit non- trivial L-space surgeries. We also recover a characterization of the Berge manifold amongst 1-bridge braid exteriors.

arXiv comment17 pages, 5 figures; v2: corrects minor errors, has a new figure (Figure 2). This is the version to appear in Compositio Mathematica

References in corpus (4)

• Floer Simple Manifolds and L-Space Intervals
• On the knot Floer homology of twisted torus knots
• Knot commensurability and the Berge conjecture
• Berge-Gabai knots and L-space satellite operations

Cited by in corpus (8)

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• Taut Foliations, Positive 3-Braids, and the L-Space Conjecture
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• Constrained knots in lens spaces
• Twist positivity, L-space knots, and concordance
• Taut foliations, braid positivity, and unknot detection
• Knot Floer homology and the fundamental group of $(1,1)$ knots