Algebraic and Geometric Topology 5 (2005), paper no. 51, pages 1315-1324.

Twisted Alexander polynomials and surjectivity of a group homomorphism

Teruaki Kitano, Masaaki Suzuki and Masaaki Wada

Abstract. If phi: G-->G' is a surjective homomorphism, we prove that the twisted Alexander polynomial of G is divisible by the twisted Alexander polynomial of G'. As an application, we show non-existence of surjective homomorphism between certain knot groups.

Keywords. Twisted Alexander polynomial, finitely presentable group, surjective homomorphism, Reidemeister torsion

AMS subject classification. Primary: 57M25. Secondary: 57M05.

E-print: arXiv:math.GT/0510224

DOI: 10.2140/agt.2005.5.1315

Submitted: 6 July 2005. Accepted: 2 September 2005. Published: 6 October 2005.

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Teruaki Kitano, Masaaki Suzuki and Masaaki Wada
Department of Mathematical and Computing Sciences, Tokyo Institute of Technology
2-12-1-W8-43 Oh-okayama, Meguro-ku, Tokyo, 152-8552 Japan

Graduate School of Mathematical Sciences, The University of Tokyo
3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914 Japan
and
Department of Information and Computer Sciences, Nara Women's University
Kita-Uoya Nishimachi, Nara, 630-8506 Japan

Email: kitano@is.titech.ac.jp, macky@ms.u-tokyo.ac.jp, wada@ics.nara-wu.ac.jp

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