Abstract
The virtual unknotting number of a virtual knot is the minimal number of crossing changes that makes the virtual knot to be the unknot, which is defined only for virtual knots virtually homotopic to the unknot. We focus on the virtual knot obtained from the standard (p,q)-torus knot diagram by replacing all crossings on one overstrand into virtual crossings and prove that its virtual unknotting number is equal to the unknotting number of the (p,q)-torus knot, that is, (p - 1)(q - 1)/2.
| Original language | English |
|---|---|
| Article number | 1750070 |
| Journal | Journal of Knot Theory and its Ramifications |
| Volume | 26 |
| Issue number | 11 |
| DOIs | |
| Publication status | Published - 2017 Oct 1 |
| Externally published | Yes |
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Keywords
- Unknotting number
- virtual knot
ASJC Scopus subject areas
- Algebra and Number Theory
Cite this
Virtual unknotting numbers of certain virtual torus knots. / Ishikawa, Masaharu; Yanagi, Hirokazu.
In: Journal of Knot Theory and its Ramifications, Vol. 26, No. 11, 1750070, 01.10.2017.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Virtual unknotting numbers of certain virtual torus knots
AU - Ishikawa, Masaharu
AU - Yanagi, Hirokazu
PY - 2017/10/1
Y1 - 2017/10/1
N2 - The virtual unknotting number of a virtual knot is the minimal number of crossing changes that makes the virtual knot to be the unknot, which is defined only for virtual knots virtually homotopic to the unknot. We focus on the virtual knot obtained from the standard (p,q)-torus knot diagram by replacing all crossings on one overstrand into virtual crossings and prove that its virtual unknotting number is equal to the unknotting number of the (p,q)-torus knot, that is, (p - 1)(q - 1)/2.
AB - The virtual unknotting number of a virtual knot is the minimal number of crossing changes that makes the virtual knot to be the unknot, which is defined only for virtual knots virtually homotopic to the unknot. We focus on the virtual knot obtained from the standard (p,q)-torus knot diagram by replacing all crossings on one overstrand into virtual crossings and prove that its virtual unknotting number is equal to the unknotting number of the (p,q)-torus knot, that is, (p - 1)(q - 1)/2.
KW - Unknotting number
KW - virtual knot
UR - http://www.scopus.com/inward/record.url?scp=85027520468&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85027520468&partnerID=8YFLogxK
U2 - 10.1142/S0218216517500705
DO - 10.1142/S0218216517500705
M3 - Article
AN - SCOPUS:85027520468
VL - 26
JO - Journal of Knot Theory and its Ramifications
JF - Journal of Knot Theory and its Ramifications
SN - 0218-2165
IS - 11
M1 - 1750070
ER -