2018/09/25 by Sam Nelson, Nelson, Sam, Kanako Oshiro +3
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.1809.09442
openalex publication_date 2018/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a new algebraic structure called local biquandles and show how colorings of oriented classical link diagrams and of broken surface diagrams are related to tribracket colorings. We define a (co)homology theory for local biquandles and show that it is isomorphic to Niebrzydowski's tribracket (co)homology. This implies that Niebrzydowski's (co)homology theory can be interpreted similary as biqandle (co)homology theory. Moreover through the isomorphism between two cohomology groups, we show that Niebrzydowski's cocycle invariants and local biquandle cocycle invariants are the same.