Geodesic
Twisted Alexander polynomials and surjectivity of a group homomorphism
Kitano, Teruaki1 ; Suzuki, Masaaki2 ; Wada, Masaaki3
1Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, 2-12-1-W8-43 Oh-okayama, Meguro-ku, Tokyo 152-8552, Japan
2Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
3Department of Information and Computer Sciences, Nara Women’s University, Kita-Uoya Nishimachi, Nara 630-8506, Japan
Algebraic and Geometric Topology, Tome 5 (2005) no. 4, pp. 1315-1324
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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.

DOI : 10.2140/agt.2005.5.1315
Keywords: twisted Alexander polynomial, finitely presentable group, surjective homomorphism, Reidemeister torsion

Kitano, Teruaki  1   ; Suzuki, Masaaki  2   ; Wada, Masaaki  3

1 Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, 2-12-1-W8-43 Oh-okayama, Meguro-ku, Tokyo 152-8552, Japan
2 Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
3 Department of Information and Computer Sciences, Nara Women’s University, Kita-Uoya Nishimachi, Nara 630-8506, Japan 
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Kitano, Teruaki; Suzuki, Masaaki; Wada, Masaaki. Twisted Alexander polynomials and surjectivity of a group homomorphism. Algebraic and Geometric Topology, Tome 5 (2005) no. 4, pp. 1315-1324. doi: 10.2140/agt.2005.5.1315

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