Twisted Alexander polynomials and surjectivity of a group homomorphism

If $φ : G \to G^{'}$ 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

Mathematical Subject Classification 2000

Primary: 57M25

Secondary: 57M05

References

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Publication

Received: 6 July 2005

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

Volume 5, issue 4 (2005)

Teruaki Kitano, Masaaki Suzuki and Masaaki Wada

Abstract