Geodesic
The Chord Index, its Definitions, Applications, and Generalizations
Canadian journal of mathematics, Tome 73 (2021) no. 3, pp. 597-621

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DOI

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.
DOI : 10.4153/S0008414X20000061
Mots-clés : virtual knot, chord index, writhe polynomial, indexed quandle, twisted knot 
Cheng, Zhiyun. The Chord Index, its Definitions, Applications, and Generalizations. Canadian journal of mathematics, Tome 73 (2021) no. 3, pp. 597-621. doi: 10.4153/S0008414X20000061
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     title = {The {Chord} {Index,} its {Definitions,} {Applications,} and {Generalizations}},
     journal = {Canadian journal of mathematics},
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     year = {2021},
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     number = {3},
     doi = {10.4153/S0008414X20000061},
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