Volume 6, issue 1 (2006)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Twisted Alexander polynomials of periodic knots

Jonathan A Hillman , Charles Livingston and Swatee Naik

Algebraic & Geometric Topology 6 (2006) 145–169

arXiv: math.GT/0412380

Abstract

Murasugi discovered two criteria that must be satisfied by the Alexander polynomial of a periodic knot. We generalize these to the case of twisted Alexander polynomials. Examples demonstrate the application of these new criteria, including to knots with trivial Alexander polynomial, such as the two polynomial 1 knots with 11 crossings.

Hartley found a restrictive condition satisfied by the Alexander polynomial of any freely periodic knot. We generalize this result to the twisted Alexander polynomial and illustrate the applicability of this extension in cases in which Hartley’s criterion does not apply.

Keywords
twisted alexander polynomial, periodic knot
Mathematical Subject Classification 2000
Primary: 57M25, 57M27
References
Forward citations
Publication
Received: 17 June 2005
Revised: 24 January 2006
Accepted: 26 January 2006
Published: 24 February 2006
Authors
Jonathan A Hillman
School of Mathematics and Statistics F07
University of Sydney
NSW 2006
Australia
Charles Livingston
Department of Mathematics
Indiana University
Bloomington IN 47405
USA
Swatee Naik
Department of Mathematics and Statistics
University of Nevada
Reno NV 89557
USA