%0 Generic %1 Litherland2002a %A Litherland, Richard A. %D 2002 %K algebra homology knot-theory quandles %T Quadratic quandles and their link invariants %U http://arxiv.org/abs/math/0207099 %X 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 Zt,t^-1/(p, t^2 + kappa t + 1), where p is a prime number and t^2 + kappa t + 1 is irreducible modulo p. For each such quandle, there is an invariant with values in the group ring ZC_p of a cyclic group of order p. We shall show that the values of this invariant all have the form Gamma_p^r p^2s for a fixed element Gamma_p of ZC_p 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.

@misc{Litherland2002a, abstract = { 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, t^2 + kappa t + 1), where p is a prime number and t^2 + kappa t + 1 is irreducible modulo p. For each such quandle, there is an invariant with values in the group ring Z[C_p] of a cyclic group of order p. We shall show that the values of this invariant all have the form Gamma_p^r p^{2s} for a fixed element Gamma_p of Z[C_p] 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. }, added-at = {2009-05-22T16:31:26.000+0200}, author = {Litherland, Richard A.}, biburl = {https://www.bibsonomy.org/bibtex/22300263cb91bfedbeda50acf44abb24b/njj}, description = {Quadratic quandles and their link invariants}, interhash = {1e6df55e969ed3e636aba45f71202457}, intrahash = {2300263cb91bfedbeda50acf44abb24b}, keywords = {algebra homology knot-theory quandles}, note = {cite arxiv:math/0207099 Comment: 19 pages, 5 figures}, timestamp = {2009-05-22T16:31:26.000+0200}, title = {Quadratic quandles and their link invariants}, url = {http://arxiv.org/abs/math/0207099}, year = 2002 }