We establish a quandle version of the twisted Alexander polynomial. We also develop a theory that reduces the size of a twisted Alexander matrix with column relations. The reduced matrix can be used to refine invariants derived from the twisted Alexander matrix.
[1] J.C. Cha: Fibred knots and twisted Alexander invariants, Trans. Amer. Math. Soc. 355 (2003), 4187–4200.
[2] R. Fenn and C. Rourke: Racks and links in codimension two, J. Knot Theory Ramifications 1 (1992),343–406.
[3] R.H. Fox: Free differential calculus. II. The isomorphism problem of groups, Ann. of Math. (2) 59 (1954), 196–210.
[4] S. Friedl and T. Kim: The Thurston norm, fibered manifolds and twisted Alexander polynomials, Topology 45 (2006), 929–953.
[5] A. Ishii and K. Oshiro: Derivatives with Alexander pairs for quandles, to appear in Fund. Math.
[6] D. Joyce: A classifying invariant of knots, the knot quandle, J. Pure Appl. Algebra 23 (1982), 37–65.
[7] H. Goda, T. Kitano and T. Morifuji: Reidemeister torsion, twisted Alexander polynomial and fibered knots, Comment. Math. Helv. 80 (2005), 51–61.
[8] H. Goda and T. Morifuji: Twisted Alexander polynomial for SL(s, C)-representations and fibered knots, C. R. Math. Acad. Sci. Soc. R. Can. 25 (2003), 97–101.
[9] X.S. Lin: Representations of knot groups and twisted Alexander polynomials, Acta Math. Sin (Engl. Ser.) 17 (2001), 361–380.
[10] S.V. Matveev: Distributive groupoids in knot theory, Mat. Sb. (N.S.) 119(161) (1982), 78–88.
[11] M. Wada: Twisted Alexander polynomial for finitely presentable groups, Topology 33 (1994), 241–256.
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