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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Twisted Alexander polynomials and surjectivity of a group homomorphism

Teruaki Kitano, Masaaki Suzuki and Masaaki Wada

Algebraic & Geometric Topology 5 (2005) 1315–1324

Erratum: Algebraic & Geometric Topology 11 (2011) 2937–2939

arXiv: math.GT/0510224

Abstract

If φ: 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
Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57M05
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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