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Strongly quasipositive quasi-alternating links and Montesinos links
Periodica Mathematica Hungarica ( IF 0.6 ) Pub Date : 2020-05-17 , DOI: 10.1007/s10998-020-00347-w
Idrissa Ba

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:

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)。
更新日期:2020-05-17
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