Algebraic & Geometric Topology

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

Jérôme Dubois and Yoshikazu Yamaguchi

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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.

Article information

Source
Algebr. Geom. Topol., Volume 12, Number 2 (2012), 791-804.

Dates
Received: 3 September 2011
Revised: 20 December 2011
Accepted: 3 January 2012
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715370

Digital Object Identifier
doi:10.2140/agt.2012.12.791

Mathematical Reviews number (MathSciNet)
MR2914618

Zentralblatt MATH identifier
1270.57020

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57M27: Invariants of knots and 3-manifolds

Keywords
Reidemeister torsion Twisted Alexander polynomial Branched cover Links Homology orientation

Citation

Dubois, Jérôme; Yamaguchi, Yoshikazu. The twisted Alexander polynomial for finite abelian covers over three manifolds with boundary. Algebr. Geom. Topol. 12 (2012), no. 2, 791--804. doi:10.2140/agt.2012.12.791. https://projecteuclid.org/euclid.agt/1513715370


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References

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