Virtual link and knot invariants from non-abelian Yang-Baxter 2-cocycle pairs

2017/07/07 by Marco A. Farinati, Farinati, Marco, Juliana García Galofre +1 · 1 citation
Mathematics · #57M25 #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.48550/arxiv.1707.02250

openalex publication_date 2017/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a given (X,S,β), where S,β\colon X× X→ X× X are set theoretical solutions of Yang-Baxter equation with a compatibility condition, we define an invariant for virtual (or classical) knots/links using non commutative 2-cocycles pairs (f,g) that generalizes the one defined in [FG2]. We also define, a group U_nc^fg=U_nc^fg(X,S,β) and functions π_f, π_g\colon X× X→ U_nc^fg(X) governing all 2-cocycles in X. We exhibit examples of computations achieved using GAP.

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