Virtual Knot Invariants From Group Biquandles and Their Cocycles
Biquandles, Yang–Baxter equation, virtual knots, cocycle invariants
Digital Object Identifier (DOI)
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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Citation / Publisher Attribution
Journal of Knot Theory and Its Ramifications, v. 18, issue 7, p. 957-972
Scholar Commons Citation
Carter, J. Scott; Silver, Daniel S.; Williams, Susan G.; Elhamdadi, Mohamed; and Saito, Masahico, "Virtual Knot Invariants From Group Biquandles and Their Cocycles" (2009). Mathematics and Statistics Faculty Publications. 128.