BIQUANDLES WITH STRUCTURES RELATED TO VIRTUAL LINKS AND TWISTED LINKS.

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 [ABSTRACT FROM AUTHOR]