Erratum to the article Twisted Alexander polynomials and surjectivity of a group homomorphism

In [1, Section 5], we considered existence of surjective homomorphisms between knot groups. In particular, the twisted Alexander polynomial was used in order to prove nonexistence of surjective homomorphisms. To be precise, we dealt with the numerator and the denominator of twisted Alexander polynomial separately and stated that there does not exist any surjective homomorphism from G.821/, G.912/, G.924/, G.939/ onto G.41/. However, the numerator and the denominator depend on the presentation of a knot, that is, each of them is not an invariant of knots, though the twisted Alexander polynomial is. We fixed the Wirtinger presentations of knot groups and discussed the numerator and the denominator of twisted Alexander polynomial separately. By that argument, we proved only nonexistence of meridian-preserving surjective homomorphisms from G.821/, G.912/, G.924/, G.939/ onto G.41/.

[1]  Yasuharu Nakae.  Taut foliations of torus knot complements , 2007 .

[2]  Vilmos Komornik,et al.  Estimation of point sources and applications to inverse problems , 2005 .

[3]  Masahiro Yamamoto,et al.  Stability estimate in a Cauchy problem for a hyperbolic equation with variable coefficients , 2005 .

[4]  Teruhisa Tsuda.  Universal Characters and q-Painlevé Systems , 2005 .

[5]  Masaaki Suzuki,et al.  A Partial Order in the Knot Table , 2005, Exp. Math..

[6]  Takashi Taniguchi.  A mean value theorem for the square of class numbers of quadratic fields , 2004 .

[7]  Takashi Taniguchi.  On proportional constants of the mean value of class numbers of quadratic extensions , 2004, math/0410060.

[8]  D. Rolfsen.  Knots and Links , 2003 .

[9]  Teruaki Kitano,et al.  Reidemeister torsion, twisted Alexander polynomial and fibered knots , 2003, math/0311155.

[10]  Xiao-Song Lin,et al.  Representations of Knot Groups and Twisted Alexander Polynomials , 2001 .

[11]  Charles Livingston,et al.  TWISTED ALEXANDER INVARIANTS, REIDEMEISTER TORSION, AND CASSON–GORDON INVARIANTS , 1999 .

[12]  Teruaki Kitano,et al.  Twisted Alexander polynomial and Reidemeister torsion , 1996 .

[13]  Masaaki Wada,et al.  Twisted Alexander polynomial for finitely presentable groups , 1994 .

[14]  H. Sakai.  Hypergeometric solution of 2 × 2q-Schlesinger system , 2004 .

[15]  L. Kauffman.  An Introduction to Knot Theory , 2001 .

[16]  Robert Lipshitz,et al.  Algebraic & Geometric Topology , 2023 .