Biquandles for Virtual Knots

Details Biquandles for Virtual Knots Biquandles for Virtual Knots

2007-03-08

arxiv.org/abs/math/0703216v1

Mathematics

Geometric Topology

24 pages, 5 figures, LaTeX document with Xy-pic generated illustrations

Scientific paper

This paper studies an algebraic invariant of virtual knots called the biquandle. The biquandle generalizes the fundamental group and the quandle of virtual knots. The approach taken in this paper to the biquandle emphasizes understanding its structure in terms of compositions of morphisms, where elementary morphisms are associated to oriented classical and virtual crossings in the diagram.

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