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ON AN INEQUALITY BETWEEN UNKNOTTING NUMBER AND CROSSING NUMBER OF LINKS

RYO HANAKI

Department of Mathematics, Nara University of Education, Takabatake, Nara, 630-8528, Japan

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and

JUNSUKE KANADOME

Graduate School of Education, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku, Tokyo, 169-8050, Japan

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https://doi.org/10.1142/S0218216510008224Cited by:0 (Source: Crossref)

Abstract

It is well-known that for any link L, twice the unknotting number of L is less than or equal to the crossing number of L. Taniyama characterized the links which satisfy the equality. We characterize the links where twice the unknotting number is equal to the crossing number minus one. As a corollary, we show that for any link L with twice the unknotting number of L is greater than or equal to the crossing number of L minus two, every minimal diagram of L realizes the unknotting number.

Keywords:

AMSC: 57M25

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