Signature of rotors
Volume 184 / 2004
Fundamenta Mathematicae 184 (2004), 79-97
MSC: Primary 57M27; Secondary 57M25.
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.
