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The twisted Alexander polynomial for finite abelian covers over three manifolds with boundary

Jérôme Dubois and Yoshikazu Yamaguchi
Algebraic & Geometric Topology 12 (2012) 791–804
DOI: 10.2140/agt.2012.12.791
Abstract

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.

Keywords
Reidemeister torsion, Twisted Alexander polynomial, Branched cover, Links, Homology orientation
Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57M27
References
Publication
Received: 3 September 2011
Revised: 20 December 2011
Accepted: 3 January 2012
Published: 17 April 2012
Authors
Jérôme Dubois
Institut de Mathématiques de Jussieu
Université Paris Diderot–Paris 7
UFR de Mathématiques
Case 7012, Bâtiment Chevaleret
75205 Paris Cedex 13
France
Yoshikazu Yamaguchi
Department of Mathematics
Tokyo Institute of Technology
2-12-1 Ookayama Meguro-ku
Tokyo 152-8551
Japan