Some knots in S× S2 with lens space surgeries

Kenneth L. Baker, Dorothy Buck, Ana G. Lecuona

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

We propose a classification of knots in S× S2 that admit a longitudinal surgery to a lens space. Any lens space obtainable by longitudinal surgery on some knot in S× S2 may be obtained from a Berge–Gabai knot in a Heegaard solid torus of S× S2, as observed by Rasmussen. We show that there are yet two other families of knots: those that lie on the fiber of a genus one fibered knot and the ‘sporadic’ knots. Assuming results of Cebanu, we are able to further conclude that these three families constitute all the doubly primitive knots in S× S2. Thus we bring the classification of lens space surgeries on knots in S× S2 in line with the Berge Conjecture about lens space surgeries on knots in S3.
Original languageEnglish
Pages (from-to)431-470
JournalCommunications in Analysis & Geometry
Volume24
Issue number3
DOIs
Publication statusPublished - 1 Jan 2016

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