Biquandle (co)homology and handlebody-links.

In this paper, we introduce the (co)homology group of a multiple conjugation biquandle. It is the (co)homology group of the prismatic chain complex, which is related to the homology of foams introduced by J. S. Carter, modulo a certain subchain complex. We construct invariants for S 1 -oriented handlebody-links using 2 -cocycles. When a multiple conjugation biquandle X × ℤ type X Y is obtained from a biquandle X using n -parallel operations, we provide a 2 -cocycle (or 3 -cocycle) of the multiple conjugation biquandle X × ℤ type X Y from a 2 -cocycle (or 3 -cocycle) of the biquandle X equipped with an X -set Y. [ABSTRACT FROM AUTHOR]