Signature of rotors

Mieczysław K. Da̧bkowski, Makiko Ishiwata, Józef H. Przytycki, Akira Yasuhara

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)79-97
Number of pages19
JournalFundamenta Mathematicae
Volume184
Issue number1-3
DOIs
Publication statusPublished - 2004 Jan 1
Externally publishedYes

Keywords

  • Branched cover
  • Conway polynomial
  • Goeritz form
  • Jones polynomial
  • Link
  • Mutation
  • Rotor
  • Seifert form
  • Signature

ASJC Scopus subject areas

  • Algebra and Number Theory

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  • Cite this

    Da̧bkowski, M. K., Ishiwata, M., Przytycki, J. H., & Yasuhara, A. (2004). Signature of rotors. Fundamenta Mathematicae, 184(1-3), 79-97. https://doi.org/10.4064/fm184-0-6