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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm184-0-6,
author = {Mieczys\l aw K. D\k abkowski and Makiko Ishiwata and J\'ozef H. Przytycki and Akira Yasuhara},
title = {Signature of rotors},
journal = {Fundamenta Mathematicae},
volume = {184},
year = {2004},
pages = {79-97},
zbl = {1079.57007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm184-0-6}
}
Mieczysław K. Dąbkowski; Makiko Ishiwata; Józef H. Przytycki; Akira Yasuhara. Signature of rotors. Fundamenta Mathematicae, Tome 184 (2004) pp. 79-97. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm184-0-6/