Geodesic
The twisted Alexander polynomial for finite abelian covers over three manifolds with boundary
Dubois, Jérôme1 ; Yamaguchi, Yoshikazu2
1Institut de Mathématiques de Jussieu, Université Paris Diderot–Paris 7, UFR de Mathématiques, Case 7012, Bâtiment Chevaleret, 75205 Paris Cedex 13, France
2Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Ookayama Meguro-ku, Tokyo 152-8551, Japan
Algebraic and Geometric Topology, Tome 12 (2012) no. 2, pp. 791-804
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We provide the twisted Alexander polynomials of finite abelian covers over three-dimensional manifolds whose boundary is a finite union of tori. This is a generalization of a well-known formula for the usual Alexander polynomial of knots in finite cyclic branched covers over the three-dimensional sphere.

DOI : 10.2140/agt.2012.12.791
Keywords: Reidemeister torsion, Twisted Alexander polynomial, Branched cover, Links, Homology orientation

Dubois, Jérôme  1   ; Yamaguchi, Yoshikazu  2

1 Institut de Mathématiques de Jussieu, Université Paris Diderot–Paris 7, UFR de Mathématiques, Case 7012, Bâtiment Chevaleret, 75205 Paris Cedex 13, France
2 Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Ookayama Meguro-ku, Tokyo 152-8551, Japan 
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Dubois, Jérôme; Yamaguchi, Yoshikazu. The twisted Alexander polynomial for finite abelian covers over three manifolds with boundary. Algebraic and Geometric Topology, Tome 12 (2012) no. 2, pp. 791-804. doi: 10.2140/agt.2012.12.791

[1] M Hirasawa, K Murasugi, On the twisted Alexander Polynomials of Knots, from: "Proceedings of Hakone Seminar on Graphs and 3–manifolds" (editor M Yamasita) (2007) 1

[2] P Kirk, C Livingston, Twisted Alexander invariants, Reidemeister torsion, and Casson–Gordon invariants, Topology 38 (1999) 635

[3] J Milnor, Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966) 358

[4] J W Milnor, Infinite cyclic coverings, from: "Conference on the Topology of Manifolds (Michigan State Univ., E. Lansing, Mich., 1967)", Prindle, Weber Schmidt, Boston (1968) 115

[5] J Porti, Mayberry–Murasugi’s formula for links in homology 3–spheres, Proc. Amer. Math. Soc. 132 (2004) 3423

[6] J P Serre, Représentations linéaires des groupes finis, Hermann (1978) 182

[7] D S Silver, S G Williams, Dynamics of twisted Alexander invariants, Topology Appl. 156 (2009) 2795

[8] V G Turaev, Reidemeister torsion in knot theory, Uspekhi Mat. Nauk 41 (1986) 97, 240

[9] V Turaev, Introduction to combinatorial torsions, , Birkhäuser (2001)

[10] V Turaev, Torsions of 3–dimensional manifolds, 208, Birkhäuser (2002)

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