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Quasi-alternating links with small determinant

Published online by Cambridge University Press:  14 July 2016

TYE LIDMAN  and
STEVEN SIVEK
TYE LIDMAN
Affiliation:
Department of Mathematics, Box 8205, NC State University, Raleigh, NC 27695-8205, U.S.A. e-mail: tlidman@ncsu.edu
STEVEN SIVEK
Affiliation:
Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544-1000, U.S.A. e-mail: ssivek@math.princeton.edu
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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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