Signature of rotors

Rotors were introduced in Graph Theory by W.Tutte. The concept was adapted to Knot Theory as a generalization of mutation by Anstee, Przytycki and Rolfsen in 1987. In this paper we show that Tristram-Levine signature is preserved by orientation-preserving rotations. Moreover, we show that any link i...

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Bibliographic Details
Published in:arXiv.org 2004-07
Main Authors: Dabkowski, Mieczyslaw K, Ishiwata, Makiko, Przytycki, Jozef H, Yasuhara, Akira
Format: Article
Language:English
Subjects:
Graph theory
Knot theory
Mutation
Orientation
Polynomials
Rotors
Online Access:Get full text
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Summary:Rotors were introduced in Graph Theory by W.Tutte. The concept was adapted to Knot Theory as a generalization of mutation by Anstee, Przytycki and Rolfsen in 1987. In this paper we show that Tristram-Levine signature is preserved by orientation-preserving rotations. Moreover, we show that any link invariant obtained from the characteristic polynomial of Goeritz matrix, including Murasugi signature, is not changed by rotations. In 2001, P. Traczyk showed that the Conway polynomials of any pair of orientation-preserving rotants coincide. But it was still an open problem if an orientation-reversing rotation preserves Conway polynomial. We show that there is a pair of orientation-reversing rotants with different Conway polynomials. This provides a negative solution to the problem.
ISSN:2331-8422