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Strongly quasipositive quasi-alternating links and Montesinos links

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Abstract

The aim of this article is to give a characterization of strongly quasipositive quasi-alternating links and detect new classes of strongly quasipositive Montesinos links and non-strongly quasipositive Montesinos links. In this direction, we show that, if L is an oriented quasi-alternating link with a quasi-alternating crossing c such that \(L_0\) is alternating (where \(L_0\) has the induced orientation), then L is definite if and only if it is strongly quasipositive (up to mirroring). We also show that if L is an oriented quasi-alternating link with a quasi-alternating crossing c such that \(L_0\) is fibred or, more generally, has a unique minimal genus Seifert surface (where \(L_0\) has the induced orientation), then L is definite if and only if it is strongly quasipositive (up to mirroring).

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Acknowledgements

I would like to thank my PhD supervisor Professor Steven Boyer for drawing my attention to the topic of the current paper and his consistent encouragement and support. I am also grateful to Kenneth Baker for his helpful comments and encouragement. I also thank the referee for many helpful comments that improved the presentation of this paper.

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  1. Department of Mathematics, University of Manitoba, Winnipeg, MB, R3T 2N2, Canada

    Idrissa Ba

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Ba, I. Strongly quasipositive quasi-alternating links and Montesinos links. Period Math Hung 82, 181–197 (2021). https://doi.org/10.1007/s10998-020-00347-w

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