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Virtual Knot Invariants from Group Biquandles and Their Cocycles

Research paper by J. Scott Carter, Mohamed Elhamdadi, Masahico Saito, Daniel S. Silver, Susan G. Williams

Indexed on: 20 Mar '07Published on: 20 Mar '07Published in: Mathematics - Geometric Topology



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.