A surgical perspective on quasi-alternating links

Liam Watson

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arXiv · 0910.0449

A surgical perspective on quasi-alternating links

Liam Watson

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Abstract

We show that quasi-alternating links arise naturally when considering surgery on a strongly invertible L-space knot (that is, a knot that yields an L-space for some Dehn surgery). In particular, we show that for many known classes of L-space knots, every sufficiently large surgery may be realized as the two-fold branched cover of a quasi-alternating link. Consequently, there is considerable overlap between L-spaces obtained by surgery on $S^3$, and L-spaces resulting as two-fold branched covers of quasi-alternating links. By adapting this approach to certain Seifert fibered spaces, it is possible to give an iterative construction for quasi-alternating Montesinos links.

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BibTeX RIS

Liam Watson. 2009-10-02. A surgical perspective on quasi-alternating links. https://arxiv.org/abs/0910.0449

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