PERIODIC VIRTUAL LINKS AND THE BINARY BRACKET POLYNOMIAL.

L. H. Kauffman defined the binary bracket polynomial of a virtual link by introducing binary labelings into the states of a virtual link diagram. We use the invariant by a slight modification, and call it the modified b-polynomial. We prove that if a virtual link K has a period pl for a prime p and a positive integer l, then the modified b-polynomial InvK (A) of K is congruent to InvK* (A) modulo p and A4pl-1 where K* is the mirror image of K. We exhibit examples of virtual links whose periods are completely determined by the invariant. [ABSTRACT FROM AUTHOR]