Signature of rotors

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

doi:10.4064/fm184-0-6

Signature of rotors

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	79-97
Number of pages	19
Journal	Fundamenta Mathematicae
Volume	184
Issue number	1-3
DOIs	https://doi.org/10.4064/fm184-0-6
Publication status	Published - 2004
Externally published	Yes

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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10.4064/fm184-0-6

Cite this

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title = "Signature of rotors",

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.",

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year = "2004",

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language = "English",

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pages = "79--97",

journal = "Fundamenta Mathematicae",

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TY - JOUR

T1 - Signature of rotors

AU - Da̧bkowski, Mieczysław K.

AU - Ishiwata, Makiko

AU - Przytycki, Józef H.

AU - Yasuhara, Akira

PY - 2004

Y1 - 2004

N2 - 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.

AB - 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.

KW - Branched cover

KW - Conway polynomial

KW - Goeritz form

KW - Jones polynomial

KW - Link

KW - Mutation

KW - Rotor

KW - Seifert form

KW - Signature

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DO - 10.4064/fm184-0-6

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VL - 184

SP - 79

EP - 97

JO - Fundamenta Mathematicae

JF - Fundamenta Mathematicae

IS - 1-3

ER -

Signature of rotors

Abstract

Keywords

ASJC Scopus subject areas

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