2018/01/22 by Atsushi Ishii, Ishii, Atsushi, Masahide Iwakiri +9
Computer Science · Mathematics · #57M25 #57M27 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1801.07602
openalex publication_date 2018/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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×ℤtypeXY is obtained from a biquandle X using n-parallel operations, we provide a 2-cocycle (or 3-cocycle) of the multiple conjugation biquandle X×ℤtypeXY from a 2-cocycle (or 3-cocycle) of the biquandle X equipped with an X-set Y.