Champanerkar and Kofman [Twisting quasi-alternating links, Proc. Amer. Math. Soc. 137(7) (2009) 2451–2458] introduced an interesting way to construct new examples of quasi-alternating links from existing ones. Actually, they proved that replacing a quasi-alternating crossing [Formula: see text] in a quasi-alternating link by a rational tangle of same type yields a new quasi-alternating link. This construction has been extended to alternating algebraic tangles and applied to characterize all quasi-alternating Montesinos links. In this paper, we extend this technique to any alternating tangle of same type as [Formula: see text]. As an application, we give new examples of quasi-alternating knots of 13 and 14 crossings. Moreover, we prove that the Jones polynomial of a quasi-alternating link that is obtained in this way has no gap if the original link has no gap in its Jones polynomial. This supports a conjecture introduced in [N. Chbili and K. Qazaqzeh, On the Jones polynomial of quasi-alternating links, Topology Appl. 264 (2019) 1–11], which states that the Jones polynomial of any prime quasi-alternating link except [Formula: see text]-torus links has no gap.

中文翻译：

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扩展准交替链接

Champanerkar 和 Kofman [扭曲准交替链接，Proc。阿米尔。数学。社会党。137(7) (2009) 2451–2458] 介绍了一种有趣的方法，可以从现有链接构建准交替链接的新示例。实际上，他们证明了用相同类型的有理缠结代替准交替链接中的准交替交叉[公式：见正文]会产生新的准交替链接。这种结构已扩展到交替代数缠结，并应用于表征所有准交替 Montesinos 链接。在本文中，我们将此技术扩展到与 [公式：见正文] 相同类型的任何交替缠结。作为一个应用，我们给出了 13 和 14 交叉的准交替结的新例子。而且，我们证明，如果原始链路在其琼斯多项式中没有间隙，则以这种方式获得的准交替链路的琼斯多项式没有间隙。这支持了 [N. Chbili 和 K. Qazaqzeh，关于准交替链路的琼斯多项式，拓扑应用。264 (2019) 1-11]，其中指出除 [公式：见文本]-环面链接之外的任何素数准交替链接的琼斯多项式都没有间隙。