Volume 10, issue 2 (2010)

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On reciprocality of twisted Alexander invariants

Jonathan A Hillman, Daniel S Silver and Susan G Williams

Algebraic & Geometric Topology 10 (2010) 1017–1026
Abstract

Given a knot and an SLnF representation of its group that is conjugate to its dual, the representation that replaces each matrix with its inverse-transpose, the associated twisted Reidemeister torsion is reciprocal. An example is given of a knot group and SL3 representation for which the twisted Reidemeister torsion is not reciprocal.

Keywords
knot, twisted Reidemeister torsion, twisted Alexander polynomial
Mathematical Subject Classification 2000
Primary: 57M25
References
Publication
Received: 18 June 2009
Accepted: 26 February 2010
Published: 26 April 2010
Authors
Jonathan A Hillman
School of Mathematics and Statistics F07
University of Sydney
Sydney, NSW 2006
Australia
http://www.maths.usyd.edu.au/u/jonh/
Daniel S Silver
Department of Mathematics and Statistics
University of South Alabama
Mobile AL 36688
USA
http://www.southalabama.edu/mathstat/personal_pages/silver/
Susan G Williams
Department of Mathematics and Statistics
University of South Alabama
Mobile AL 36688
USA
http://www.southalabama.edu/mathstat/personal_pages/williams/