Browsing by Subject "SOLID TORI"

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    (1,1) L-space knots
    (COMPOSITIO MATHEMATICA, 2018-05-01) Greene, JE; Lewallen, S; Vafaee, F
    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.
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    Berge–Gabai knots and L–space satellite operations
    (Algebraic & Geometric Topology, 2015-01-15) Hom, J; Lidman, T; Vafaee, F
    © 2014 Mathematical Sciences Publishers. All rights reserved. Let P(K) be a satellite knot where the pattern P is a Berge–Gabai knot (ie a knot in the solid torus with a nontrivial solid torus Dehn surgery) and the companion K is a nontrivial knot in S3. We prove that P(K) is an L–space knot if and only if K is an L–space knot and P is sufficiently positively twisted relative to the genus of K. This generalizes the result for cables due to Hedden [13] and Hom [17].