2011/06/01 by Sam Nelson, Nelson, Sam, Katie Pelland +1
Mathematics · #57M25 #57M27 #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.1106.0336
openalex publication_date 2011/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce an associative algebra Z[X,S] associated to a birack shadow and define enhancements of the birack counting invariant for classical knots and links via representations of Z[X,S] known as shadow modules. We provide examples which demonstrate that the shadow module enhanced invariants are not determined by the Alexander polynomial or the unenhanced birack counting invariants.