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Brunnian local moves of knots and Vassiliev invariants

100%

Yasuhara A.

Fundamenta Mathematicae

2006

tom 190

nr 1

289-297

K. Habiro gave a neccesary and sufficient condition for knots to have the same Vassiliev invariants in terms of $C_k$-moves. In this paper we give another geometric condition in terms of Brunnian local moves. The proof is simple and self-contained.

Signature of rotors

51%

Dąbkowski M., Ishiwata M., Przytycki J., Yasuhara A.

Fundamenta Mathematicae

2004

tom 184

nr 1

79-97

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.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Yasuhara A.

1 Dąbkowski M.

1 Ishiwata M.

1 Przytycki J.

1 2006

1 2004

Wyniki wyszukiwania

Brunnian local moves of knots and Vassiliev invariants

Signature of rotors