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Quasi-alternating links with small determinant

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Title: Quasi-alternating links with small determinant
Authors: Lidman, T
Sivek, S
Item Type: Journal Article
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.
Issue Date: 14-Jul-2016
Date of Acceptance: 1-Jun-2016
URI: http://hdl.handle.net/10044/1/48957
DOI: https://dx.doi.org/10.1017/S0305004116000578
ISSN: 0305-0041
Publisher: Cambridge University Press
Start Page: 319
End Page: 336
Journal / Book Title: Mathematical Proceedings of the Cambridge Philosophical Society
Volume: 162
Issue: 02
Copyright Statement: © Cambridge Philosophical Society 2016
Keywords: math.GT
57M25, 57M27, 57R58
0101 Pure Mathematics
Publication Status: Published
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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