A NOTE ON DEGREES OF TWISTED ALEXANDER POLYNOMIALS II

Title & Authors
A NOTE ON DEGREES OF TWISTED ALEXANDER POLYNOMIALS II
Morifuji, Takayuki; Suzuki, Masaaki;

Abstract
In this short note we discuss degrees of twisted Alexander polynomials and demonstrate an explicit example of a closed 3-manifold which is related to the degree formula due to Friedl, Kim and Kitayama.
Keywords
twisted Alexander polynomial;knot group;zero-surgery;
Language
English
Cited by
References
1.
S. Friedl, T. Kim, and T. Kitayama, Poincare duality and degrees of twisted Alexander polynomials, Indiana Univ. Math. J. (to appear).

2.
S. Friedl and S. Vidussi, A survey of twisted Alexander polynomials, The Mathematics of Knots: Theory and Application (Contributions in Mathematical and Computational Sciences), eds. Markus Banagl and Denis Vogel (2010), 45-94.

3.
T. Kim and T. Morifuji, Twisted Alexander polynomials and character varieties of 2-bridge knot groups, Internat. J. Math. 23 (2012), 1250022, 18 pp.

4.
T. Kitano, Twisted Alexander polynomial and Reidemeister torsion, Pacific J. Math. 174 (1996), no. 2, 431-442.

5.
T. Kitano and T. Morifuji, Divisibility of twisted Alexander polynomials and fibered knots, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 4 (2005), no. 1, 179-186.

6.
T. Kitano and M. Suzuki, On the number of SL(2; \${\mathbb{Z}}\$/\$p{\mathbb{Z}}\$)-representations of knot groups, J. Knot Theory Ramifications 21 (2012), no. 1, 1250003, 18 pp.

7.
X. S. Lin, Representations of knot groups and twisted Alexander polynomials, Acta Math. Sin. (Engl. Ser.) 17 (2001), no. 3, 361-380.

8.
J. Milnor, Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966), 358-426.

9.
T. Morifuji, Twisted Alexander polynomials of twist knots for nonabelian representations, Bull. Sci. Math. 132 (2008), no. 5, 439-453.

10.
T. Morifuji, A note on degrees of twisted Alexander polynomials, RIMS Kokyuroku 1747 (2011), 121-125.

11.
R. Riley, Nonabelian representations of 2-bridge knot groups, Quart. J. Math. Oxford Ser. (2) 35 (1984), 191-208.

12.
M. Wada, Twisted Alexander polynomial for finitely presentable groups, Topology 33 (1994), no. 2, 241-256.