Signature of rotors

Volume 184 / 2004

Mieczys/law K. D/abkowski, Makiko Ishiwata, Józef H. Przytycki, Akira Yasuhara Fundamenta Mathematicae 184 (2004), 79-97 MSC: Primary 57M27; Secondary 57M25. DOI: 10.4064/fm184-0-6


Rotors were introduced as a generalization of mutation by Anstee, Przytycki and Rolfsen in 1987. In this paper we show that the Tristram–Levine signature is preserved by orientation-preserving rotations. Moreover, we show that any link invariant obtained from the characteristic polynomial of the Goeritz matrix, including the Murasugi–Trotter signature, is not changed by rotations. In 2001, P. Traczyk showed that the Conway polynomials of any pair of orientation-preserving rotants coincide. We show that there is a pair of orientation-reversing rotants with different Conway polynomials.


  • Mieczys/law K. D/abkowskiDepartment of Mathematics
    University of Texas at Dallas
    Richardson, TX 75083-0688, U.S.A.
  • Makiko IshiwataDepartment of Mathematics
    Tokyo Woman's Christian University
    Zempukuji 2-6-1, Suginamiku
    Tokyo 167-8585, Japan
  • Józef H. PrzytyckiDepartment of Mathematics
    The George Washington University
    Washington, DC 20052, U.S.A.
  • Akira YasuharaDepartment of Mathematics
    Tokyo Gakugei University
    Nukuikita 4-1-1, Koganei
    Tokyo 184-8501, Japan

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