Biquandles with structures related to virtual links and twisted links

Details Biquandles with structures related to virtual links and twisted links Biquandles with structures related to virtual links and twisted links

2011-09-24

arxiv.org/abs/1109.5251v1

Mathematics

Geometric Topology

Scientific paper

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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