2002/07/11 by R. A. Litherland, Richard A. Litherland, Litherland, Richard A.
Mathematics · #55N99 (secondary) #57M25 (primary) #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.GT #math.QA #msc:55N99 #msc:57M25
paper · pdf · doi:10.48550/arxiv.math/0207099
19 pages, 5 figures
arxiv created 2002/07/11 · openalex publication_date 2002/07/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Carter, Jelsovsky, Kamada, Langford and Saito have defined an invariant of classical links associated to each element of the second cohomology of a finite quandle. We study these invariants for Alexander quandles of the form Z[t,t-1]/(p, t2 + kappa t + 1), where p is a prime number and t2 + kappa t + 1 is irreducible modulo p. For each such quandle, there is an invariant with values in the group ring Z[Cp] of a cyclic group of order p. We shall show that the values of this invariant all have the form Gammapr p2s for a fixed element Gammap of Z[Cp] and integers r >= 0 and s > 0. We also describe some machine computations, which lead us to conjecture that the invariant is determined by the Alexander module of the link. This conjecture is verified for all torus and two-bridge knots.