2015/08/26 by Sam Nelson, Nelson, Sam, Michael E. Orrison +3 · 3 citations
Mathematics · #57M25 #57M27 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.1508.06573
openalex publication_date 2015/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a new class of quantum enhancements we call biquandle brackets, which are customized skein invariants for biquandle colored links.Quantum enhancements of biquandle counting invariants form a class of knot and link invariants that includes biquandle cocycle invariants and skein invariants such as the HOMFLY-PT polynomial as special cases, providing an explicit unification of these apparently unrelated types of invariants. We provide examples demonstrating that the new invariants are not determined by the biquandle counting invariant, the knot quandle, the knot group or the traditional skein invariants.