#### 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 ${SL}_{n}\mathbb{F}$ 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 ${SL}_{3}ℤ$ representation for which the twisted Reidemeister torsion is not reciprocal.

##### Keywords
knot, twisted Reidemeister torsion, twisted Alexander polynomial
Primary: 57M25
##### 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/