On non-self local moves

Yasutaka Nakanishi; Tetsuo Shibuya; Tatsuya Tsukamoto; Akira Yasuhara

doi:10.1142/S0218216511010097

On non-self local moves

Yasutaka Nakanishi^*, Tetsuo Shibuya, Tatsuya Tsukamoto, Akira Yasuhara

^*Corresponding author for this work

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

Abstract

Gusarov and Habiro introduced a C _m move, that is strongly related to Vassiliev invariants. In this note, we study a special kind of C _m move, called a non-self C _m move. We show that two links can be transformed into each other by a finite sequence of non-self C _m moves if and only if (1) the two links can be transformed into each other by a finite sequence of C _m moves, and (2) the knot types of corresponding components coincide.

Original language	English
Article number	1250055
Journal	Journal of Knot Theory and its Ramifications
Volume	21
Issue number	4
DOIs	https://doi.org/10.1142/S0218216511010097
Publication status	Published - 2012 Apr
Externally published	Yes

Keywords

Local move
knot type
linking number

ASJC Scopus subject areas

Algebra and Number Theory

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10.1142/S0218216511010097

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abstract = "Gusarov and Habiro introduced a C m move, that is strongly related to Vassiliev invariants. In this note, we study a special kind of C m move, called a non-self C m move. We show that two links can be transformed into each other by a finite sequence of non-self C m moves if and only if (1) the two links can be transformed into each other by a finite sequence of C m moves, and (2) the knot types of corresponding components coincide.",

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author = "Yasutaka Nakanishi and Tetsuo Shibuya and Tatsuya Tsukamoto and Akira Yasuhara",

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AU - Nakanishi, Yasutaka

AU - Shibuya, Tetsuo

AU - Tsukamoto, Tatsuya

AU - Yasuhara, Akira

PY - 2012/4

Y1 - 2012/4

N2 - Gusarov and Habiro introduced a C m move, that is strongly related to Vassiliev invariants. In this note, we study a special kind of C m move, called a non-self C m move. We show that two links can be transformed into each other by a finite sequence of non-self C m moves if and only if (1) the two links can be transformed into each other by a finite sequence of C m moves, and (2) the knot types of corresponding components coincide.

AB - Gusarov and Habiro introduced a C m move, that is strongly related to Vassiliev invariants. In this note, we study a special kind of C m move, called a non-self C m move. We show that two links can be transformed into each other by a finite sequence of non-self C m moves if and only if (1) the two links can be transformed into each other by a finite sequence of C m moves, and (2) the knot types of corresponding components coincide.

KW - Local move

KW - knot type

KW - linking number

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JF - Journal of Knot Theory and its Ramifications

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ER -

On non-self local moves

Abstract

Keywords

ASJC Scopus subject areas

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