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Virtual Knot Invariants from Group Biquandles and Their Cocycles

J. Scott Carter·Mohamed Elhamdadi·Masahico Saito·Daniel S. Silver·Susan G. Williams
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Abstract

A group-theoretical method, via Wada's representations, is presented to distinguish Kishino's virtual knot from the unknot. Biquandles are constructed for any group using Wada's braid group representations. Cocycle invariants for these biquandles are studied. These invariants are applied to show the non-existence of Alexander numberings and checkerboard colorings.

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J. Scott Carter, Mohamed Elhamdadi, Masahico Saito, Daniel S. Silver, Susan G. Williams. 2007-03-20. Virtual Knot Invariants from Group Biquandles and Their Cocycles. https://arxiv.org/abs/math/0703594

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