An estimate for the unknotting numbers of torus knots

Shinji Fukuhara; Yukio Matsumoto; Osamu Saeki

doi:10.1016/0166-8641(91)90093-2

An estimate for the unknotting numbers of torus knots

Shinji Fukuhara, Yukio Matsumoto, Osamu Saeki

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Abstract

In this note we present an estimate for the unknotting numbers of torus knots, which is an improvement of results by Murasugi (1965), Weintraub (1979), Yamamoto (1982), Boileau and Weber (1986) and Shibuya (1986). As a corollary, we show that Milnor's conjecture (1968) is true for torus knots of type (2,q), (3,4), (3,5), (3,7), (3,8), (3,10) and (4,5). For torus knots of type (2,q), (3,4) and (3,5), this has already been known.

Original language	English
Pages (from-to)	293-299
Number of pages	7
Journal	Topology and its Applications
Volume	38
Issue number	3
DOIs	https://doi.org/10.1016/0166-8641(91)90093-2
Publication status	Published - Mar 25 1991
Externally published	Yes

All Science Journal Classification (ASJC) codes

Geometry and Topology

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10.1016/0166-8641(91)90093-2

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abstract = "In this note we present an estimate for the unknotting numbers of torus knots, which is an improvement of results by Murasugi (1965), Weintraub (1979), Yamamoto (1982), Boileau and Weber (1986) and Shibuya (1986). As a corollary, we show that Milnor's conjecture (1968) is true for torus knots of type (2,q), (3,4), (3,5), (3,7), (3,8), (3,10) and (4,5). For torus knots of type (2,q), (3,4) and (3,5), this has already been known.",

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AU - Fukuhara, Shinji

AU - Matsumoto, Yukio

AU - Saeki, Osamu

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Y1 - 1991/3/25

N2 - In this note we present an estimate for the unknotting numbers of torus knots, which is an improvement of results by Murasugi (1965), Weintraub (1979), Yamamoto (1982), Boileau and Weber (1986) and Shibuya (1986). As a corollary, we show that Milnor's conjecture (1968) is true for torus knots of type (2,q), (3,4), (3,5), (3,7), (3,8), (3,10) and (4,5). For torus knots of type (2,q), (3,4) and (3,5), this has already been known.

AB - In this note we present an estimate for the unknotting numbers of torus knots, which is an improvement of results by Murasugi (1965), Weintraub (1979), Yamamoto (1982), Boileau and Weber (1986) and Shibuya (1986). As a corollary, we show that Milnor's conjecture (1968) is true for torus knots of type (2,q), (3,4), (3,5), (3,7), (3,8), (3,10) and (4,5). For torus knots of type (2,q), (3,4) and (3,5), this has already been known.

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An estimate for the unknotting numbers of torus knots

Abstract

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