Signature of rotors

Mieczysław K. Dąbkowski¹, Makiko Ishiwata², Józef H. Przytycki³, Akira Yasuhara⁴
Fund. Math. 184 (2004), 79-97
doi:10.4064/fm184-0-6

Abstract: 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.

MSC (2000): Primary 57M27; Secondary 57M25.
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Department of Mathematics
University of Texas at Dallas
Richardson, TX 75083-0688, U.S.A.
Department of Mathematics
Tokyo Woman's Christian University
Zempukuji 2-6-1, Suginamiku
Tokyo 167-8585, Japan
Department of Mathematics
The George Washington University
Washington, DC 20052, U.S.A.
Department of Mathematics
Tokyo Gakugei University
Nukuikita 4-1-1, Koganei
Tokyo 184-8501, Japan