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$(1,1)$ L-space knots

Part of: Low-dimensional topology

Published online by Cambridge University Press:  20 March 2018

Joshua Evan Greene ,
Sam Lewallen  and
Faramarz Vafaee
Joshua Evan Greene
Affiliation:
Department of Mathematics, Boston College, Chestnut Hill, MA 02467, USA email joshua.greene@bc.edu
Sam Lewallen
Affiliation:
Princeton Neuroscience Institute, Princeton University, Princeton, NJ 08544, USA email lewallen@princeton.edu
Faramarz Vafaee
Affiliation:
Mathematics Department, California Institute of Technology, Pasadena, CA 91125, USA email vafaee@caltech.edu
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Abstract

We characterize the $(1,1)$ knots in the 3-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 among 1-bridge braid exteriors.

Keywords

Floer homologyL-spaceDehn surgery

MSC classification

Primary: 57M27: Invariants of knots and 3-manifolds

Information

Type
Research Article
Information
Compositio Mathematica , Volume 154 , Issue 5 , May 2018 , pp. 918 - 933
Copyright
© The Authors 2018 

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