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Quasi-alternating links with small determinant
Published online by Cambridge University Press: 14 July 2016
Abstract
Quasi-alternating links of determinant 1, 2, 3 and 5 were previously classified by Greene and Teragaito, who showed that the only such links are two-bridge. In this paper, we extend this result by showing that all quasi-alternating links of determinant at most 7 are connected sums of two-bridge links, which is optimal since there are quasi-alternating links not of this form for all larger determinants. We achieve this by studying their branched double covers and characterising distance-one surgeries between lens spaces of small order, leading to a classification of formal L-spaces with order at most 7.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 162 , Issue 2 , March 2017 , pp. 319 - 336
- Copyright
- Copyright © Cambridge Philosophical Society 2016
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