#### Volume 5, issue 4 (2005)

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Twisted Alexander polynomials and surjectivity of a group homomorphism

### Teruaki Kitano, Masaaki Suzuki and Masaaki Wada

Algebraic & Geometric Topology 5 (2005) 1315–1324
 arXiv: math.GT/0510224
##### Abstract

If $\phi :\phantom{\rule{0.3em}{0ex}}G\to {G}^{\prime }$ is a surjective homomorphism, we prove that the twisted Alexander polynomial of $G$ is divisible by the twisted Alexander polynomial of ${G}^{\prime }$. 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
Primary: 57M25
Secondary: 57M05
##### Publication
Accepted: 2 September 2005
Published: 6 October 2005
##### Authors
 Teruaki Kitano Department of Mathematical and Computing Sciences Tokyo Institute of Technology 2-12-1-W8-43 Oh-okayama Meguro-ku Tokyo 152-8552 Japan Masaaki Suzuki Graduate School of Mathematical Sciences The University of Tokyo 3-8-1 Komaba Meguro-ku Tokyo 153-8914 Japan Masaaki Wada Department of Information and Computer Sciences Nara Women’s University Kita-Uoya Nishimachi Nara 630-8506 Japan