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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

DOI: 10.2140/agt.2005.5.1315

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

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