Unknotting numbers of diagrams of a given nontrivial knot are unbounded

Kouki Taniyama

doi:10.1142/S0218216509007361

Unknotting numbers of diagrams of a given nontrivial knot are unbounded

Kouki Taniyama^*

^*Corresponding author for this work

School of Education

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

9 Citations (Scopus)

Abstract

We show that for any nontrivial knot K and any natural number n, there is a diagram D of K such that the unknotting number of D is greater than or equal to n. It is well-known that twice the unknotting number of K is less than or equal to the crossing number of K minus one. We show that the equality holds only when K is a (2, p)-torus knot.

Original language	English
Pages (from-to)	1049-1063
Number of pages	15
Journal	Journal of Knot Theory and its Ramifications
Volume	18
Issue number	8
DOIs	https://doi.org/10.1142/S0218216509007361
Publication status	Published - 2009 Aug

Keywords

Crossing number.
Knot
Unknotting number
Unknotting number of diagram

ASJC Scopus subject areas

Algebra and Number Theory

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10.1142/S0218216509007361

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abstract = "We show that for any nontrivial knot K and any natural number n, there is a diagram D of K such that the unknotting number of D is greater than or equal to n. It is well-known that twice the unknotting number of K is less than or equal to the crossing number of K minus one. We show that the equality holds only when K is a (2, p)-torus knot.",

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AB - We show that for any nontrivial knot K and any natural number n, there is a diagram D of K such that the unknotting number of D is greater than or equal to n. It is well-known that twice the unknotting number of K is less than or equal to the crossing number of K minus one. We show that the equality holds only when K is a (2, p)-torus knot.

KW - Crossing number.

KW - Knot

KW - Unknotting number

KW - Unknotting number of diagram

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JF - Journal of Knot Theory and its Ramifications

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ER -

Unknotting numbers of diagrams of a given nontrivial knot are unbounded

Abstract

Keywords

ASJC Scopus subject areas

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