Volume 13 (2008)

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Twisted Alexander polynomials and a partial order on the set of prime knots

Teruaki Kitano and Masaaki Suzuki

Geometry & Topology Monographs 13 (2008) 307–321

DOI: 10.2140/gtm.2008.13.307

arXiv: 0904.0810

Abstract

We give a survey of some recent papers by the authors and Masaaki Wada relating the twisted Alexander polynomial with a partial order on the set of prime knots. We also give examples and pose open problems.

Dedicated to Fred Cohen on the occasion of his 60th birthday

Keywords

twisted Alexander polynomial, finitely presentable group, surjective homomorphism, prime knot, partial order

Mathematical Subject Classification

Primary: 57M25

Secondary: 57M05

References
Publication

Received: 31 May 2006
Revised: 19 September 2007
Accepted: 26 September 2007
Published: 25 February 2008

Authors
Teruaki Kitano
Department of Information Systems Science
Faculty of Engineering
Soka University
Tokyo, 192-8577
Japan
Masaaki Suzuki
Department of Mathematics
Akita University
Akita, 010-8502
Japan