On reciprocality of twisted Alexander invariants

Hillman, Jonathan A; Silver, Daniel S; Williams, Susan G

doi:10.2140/agt.2010.10.1017

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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

DOI: 10.2140/agt.2010.10.1017

Abstract

Given a knot and an ${SL}_{n} F$ 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

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/

Volume 10, issue 2 (2010)