Quasi-alternating links with small determinant
Geometric Topology
2017-02-07 v1
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 characterizing distance-one surgeries between lens spaces of small order, leading to a classification of formal L-spaces with order at most 7.
Keywords
Cite
@article{arxiv.1507.04705,
title = {Quasi-alternating links with small determinant},
author = {Tye Lidman and Steven Sivek},
journal= {arXiv preprint arXiv:1507.04705},
year = {2017}
}