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 $$L_0$$ L 0 is alternating (where $$L_0$$ 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 $$L_0$$ L 0 is fibred or, more generally, has a unique minimal genus Seifert surface (where $$L_0$$ L 0 has the induced orientation), then L is definite if and only if it is strongly quasipositive (up to mirroring).

中文翻译：

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强拟正拟交替链接和蒙特西诺链接

本文的目的是给出强准正准交替链接的特征，并检测强准正蒙特西诺链接和非强准正蒙特西诺链接的新类别。在这个方向上，我们表明，如果 L 是一个定向的准交替链路，具有一个准交替交叉点 c，使得 $$L_0$$ L 0 是交替的（其中 $$L_0$$ L 0 具有诱导方向），那么 L 是确定的当且仅当它是强拟正的（直到镜像）。我们还表明，如果 L 是具有准交替交叉点 c 的定向准交替链接，使得 $$L_0$$ L 0 是纤维状的，或者更一般地说，具有唯一的最小属 Seifert 曲面（其中 $$L_0$$ L 0 具有诱导取向），则 L 是确定的当且仅当它是强拟正的（直到镜像）。