A surgical perspective on quasi-alternating links

Details A surgical perspective on quasi-alternating links A surgical perspective on quasi-alternating links

2009-10-02

arxiv.org/abs/0910.0449v1

Mathematics

Geometric Topology

16 pages, 12 figures

Scientific paper

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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