Virtual Knot Invariants from Group Biquandles and Their Cocycles

Details Virtual Knot Invariants from Group Biquandles and Their Cocycles Virtual Knot Invariants from Group Biquandles and Their Cocycles

2007-03-20

arxiv.org/abs/math/0703594v1

Mathematics

Geometric Topology

14 pages, 8 figures

Scientific paper

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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