Qazaqzeh, Khaled; Chbili, Nafaa A new obstruction of quasialternating links. (English) Zbl 1322.57013 Algebr. Geom. Topol. 15, No. 3, 1847-1862 (2015). Quasi-alternating links are a generalization of alternating links from the viewpoint of Heegaard Floer homology theory. The definition is recursive, so it is not easy to determine whether a given knot or link is quasi-alternating or not, in general. There are several known properties of quasi-alternating links. For example, the double branched cover is an \(L\)-space, and the knot Floer homology, the reduced Khovanov homology, and the reduced odd Khovanov homology are all thin. Hence these can be obstructions for a knot or link to be quasi-alternating.The paper under review gives a remarkably simple obstruction. It claims that for any quasi-alternating link, the degree of its \(Q\)-polynomial is less than its determinant. As an application, it is shown that only finitely many Kanenobu knots can be quasi-alternating.The last part of the paper contains an interesting conjecture which claims that for a quasi-alternating link, the span of the Jones polynomial is less than or equal to the determinant. In fact, the authors prove this conjecture for closed \(3\)-braids. Reviewer: Masakazu Teragaito (Hiroshima) Cited in 2 ReviewsCited in 7 Documents MSC: 57M27 Invariants of knots and \(3\)-manifolds (MSC2010) 57M25 Knots and links in the \(3\)-sphere (MSC2010) Keywords:quasi-alternating link; \(Q\)-polynomial; determinant; Kanenobu knot Software:KnotInfo; Knot Atlas; KnotTheory; Khoho PDFBibTeX XMLCite \textit{K. Qazaqzeh} and \textit{N. Chbili}, Algebr. Geom. Topol. 15, No. 3, 1847--1862 (2015; Zbl 1322.57013) Full Text: DOI arXiv References: [1] J A Baldwin, Heegaard Floer homology and genus one, one-boundary component open books, J. 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