Biquandle (co)homology and handlebody-links
Ishii, Atsushi · Iwakiri, Masahide · Kamada, Seiichi · Kim, Jieon · Matsuzaki, Shosaku · Oshiro, Kanako
Original · EN
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 S¹-oriented handlebody-links using 2-cocycles. When a multiple conjugation biquandle X is obtained from a biquandle X using n-parallel operations, we provide a 2-cocycle (or 3-cocycle) of the multiple conjugation biquandle X from a 2-cocycle (or 3-cocycle) of the biquandle X equipped with an X-set Y.
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