The Chord Index, its Definitions, Applications, and Generalizations

Cheng Zhiyun

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The Chord Index, its Definitions, Applications, and Generalizations

机译：Chord指数，其定义，应用程序和概括

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In this paper, we study the chord index of virtual knots, which can be thought of as an extension of the chord parity. We show how to use the chord index to enhance the quandle coloring invariants. The notion of indexed quandle is introduced, which generalizes the quandle idea. Some applications of this new invariant is discussed. We also study how to define a generalized chord index via a fixed finite biquandle. Finally, the chord index and its applications in twisted knot theory are discussed.

机译：在本文中，我们研究了虚拟节点的弦指数，它可以被认为是弦奇偶性的延伸。我们展示了如何使用chord索引来增强量子着色不变量。引入了索引量子的概念，推广了量子概念。讨论了这种新不变量的一些应用。我们还研究了如何通过固定的有限双量子定义广义弦指数。最后讨论了弦指数及其在扭结理论中的应用。

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来源
《Canadian Journal of Mathematics》 |2021年第3期|共25页
作者
Cheng Zhiyun;
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作者单位

Beijing Normal Univ Sch Math Sci Lab Math &

Complex Syst Beijing 100875 Peoples R China;

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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
virtual knot; chord index; writhe polynomial; indexed quandle; twisted knot;

机译：虚拟结;弦指数;Writhe多项式;索引Quandle;扭曲结;

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The Chord Index, its Definitions, Applications, and Generalizations

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