Signature of rotors

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

Fundamenta Mathematicae (2004)

  • Volume: 184, Issue: 1, page 79-97
  • ISSN: 0016-2736

Abstract

top
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.

How to cite

top

Mieczysław K. Dąbkowski, et al. "Signature of rotors." Fundamenta Mathematicae 184.1 (2004): 79-97. <http://eudml.org/doc/282784>.

@article{MieczysławK2004,
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.},
author = {Mieczysław K. Dąbkowski, Makiko Ishiwata, Józef H. Przytycki, Akira Yasuhara},
journal = {Fundamenta Mathematicae},
keywords = {link; mutation; rotor; signature; Seifert form; Goeritz form; Conway polynomial},
language = {eng},
number = {1},
pages = {79-97},
title = {Signature of rotors},
url = {http://eudml.org/doc/282784},
volume = {184},
year = {2004},
}

TY - JOUR
AU - Mieczysław K. Dąbkowski
AU - Makiko Ishiwata
AU - Józef H. Przytycki
AU - Akira Yasuhara
TI - Signature of rotors
JO - Fundamenta Mathematicae
PY - 2004
VL - 184
IS - 1
SP - 79
EP - 97
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.
LA - eng
KW - link; mutation; rotor; signature; Seifert form; Goeritz form; Conway polynomial
UR - http://eudml.org/doc/282784
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.