Biquandles with structures related to virtual links and twisted links

Naoko Kamada; Seiichi Kamada

doi:10.1142/s0218216512400068

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arXiv · 1109.5251

Biquandles with structures related to virtual links and twisted links

Naoko Kamada·Seiichi Kamada

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Abstract

We introduce two kinds of structures, called v-structures and t-structures, on biquandles. These structures are used for colorings of diagrams of virtual links and twisted links such that the numbers of colorings are invariants. Given a biquandle or a quandle, we give a method of constructing a biquandle with these structures. Using the numbers of colorings, we show that Bourgoin's twofoil and non-orientable virtual $m$-foils do not represent virtual links.

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Naoko Kamada, Seiichi Kamada. 2011-09-24. Biquandles with structures related to virtual links and twisted links. https://doi.org/10.1142/s0218216512400068

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