论文标题
扩展准偏置链接
Extending Quasi-Alternating Links
论文作者
论文摘要
Champanerkar和Kofman提出了一种有趣的方式，用于构建现有链接的新示例。实际上，他们证明，通过相同类型的合理纠缠替换了准偏置链接中的准偏跨C会产生新的准偏置链接。该结构已扩展到交替的代数缠结，并应用于表征所有准替代的蒙特西诺斯链路。在本文中，我们将此技术扩展到与C相同类型的任何交替纠结。作为应用程序，我们提供了13和14个交叉点的准替代结的新示例。此外，我们证明，如果原始链接在其琼斯多项式中没有差距，则以这种方式获得的准偏置链接的琼斯多项式没有差距。这支持了Arxiv：1810.11773 [Math.gt]中引入的猜想，该猜想指出，除了（2; n）-torus链接外，任何主要的准替代链接的琼斯多项式都没有间隙。
Champanerkar and Kofman introduced an interesting way to construct new examples of quasi-alternating links from existing ones. Actually, they proved that replacing a quasi-alternating crossing c 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 c. 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 arXiv:1810.11773 [math.GT], which states that Jones polynomial of any prime quasi-alternating link except (2; n)-torus link has no gap.
