2019/10/09 by Marco A. Farinati, Farinati, Marco, Juliana García Galofre +1
Mathematics · #57M25 #57M27 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1910.04042
openalex publication_date 2019/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a biquandle (X, S), a function τ with certain compatibility and a pair of \em non commutative cocyles f,h:X × X→ G with values in a non necessarily commutative group G, we give an invariant for singular knots / links. Given (X,S,τ), we also define a universal group Uncfh(X) and universal functions governing all 2-cocycles in X, and exhibit examples of computations. When the target group is abelian, a notion of \em abelian cocycle pair is given and the "state sum" is defined for singular knots/links. Computations generalizing linking number for singular knots are given. As for virtual knots, a "self-linking number" may be defined for singular knots