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Twisted Alexander
polynomials of periodic knots
Jonathan A Hillman , Charles Livingston and Swatee Naik |
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Algebraic & Geometric Topology 6 (2006) 145–169
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arXiv: math.GT/0412380 |
Abstract |
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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
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Mathematical Subject Classification 2000
Primary: 57M25, 57M27
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References |
Forward citations |
Publication
Received: 17 June 2005
Revised: 24 January 2006
Accepted: 26 January 2006
Published: 24 February 2006
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Authors |
| Jonathan A Hillman | |
| School of Mathematics and Statistics
F07 University of Sydney NSW 2006 Australia |
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| Charles Livingston | |
| Department of Mathematics Indiana University Bloomington IN 47405 USA |
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| Swatee Naik | |
| Department of Mathematics and
Statistics University of Nevada Reno NV 89557 USA |
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