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Local-moves on knots and products of knots II. / Kauffman, Louis H.; Ogasa, Eiji.

в: Journal of Knot Theory and its Ramifications, Том 30, № 10, 2140006, 01.09.2021.

Результаты исследований: Научные публикации в периодических изданияхстатьяРецензирование

Harvard

Kauffman, LH & Ogasa, E 2021, 'Local-moves on knots and products of knots II', Journal of Knot Theory and its Ramifications, Том. 30, № 10, 2140006. https://doi.org/10.1142/S021821652140006X

APA

Kauffman, L. H., & Ogasa, E. (2021). Local-moves on knots and products of knots II. Journal of Knot Theory and its Ramifications, 30(10), [2140006]. https://doi.org/10.1142/S021821652140006X

Vancouver

Kauffman LH, Ogasa E. Local-moves on knots and products of knots II. Journal of Knot Theory and its Ramifications. 2021 сент. 1;30(10):2140006. doi: 10.1142/S021821652140006X

Author

Kauffman, Louis H. ; Ogasa, Eiji. / Local-moves on knots and products of knots II. в: Journal of Knot Theory and its Ramifications. 2021 ; Том 30, № 10.

BibTeX

@article{3d0f33eb7a624682a1b8dcaec1e79318,
title = "Local-moves on knots and products of knots II",
abstract = "We use the terms, knot product and local-move, as defined in the text of this paper. Let n be an integer 3. Let n be the set of simple spherical n-knots in Sn+2. Let m be an integer 4. We prove that the map j: 2m →2m+4 is bijective, where j(K) = KS - Hopf, and Hopf denotes the Hopf link. Let J and K be 1-links in S3. Suppose that J is obtained from K by a single pass-move, which is a local-move on 1-links. Let k be a positive integer. Let P S - QS - k denote the knot product P S - Q S - ⋯ S - Qk. We prove the following: The (4k + 1)-dimensional submanifold JS - HopfS - k S S4k+3 is obtained from KS - HopfS - k by a single (2k+1, 2k+1)-pass-move, which is a local-move on (4k + 1)-submanifolds contained in S4k+3. See the body of this paper for the definitions of all local-moves in this abstract. We prove the following: Let a,b,a',b', and k be positive integers. If the (a,b) torus link is pass-move-equivalent to the (a',b') torus link, then the Brieskorn manifolds, ς(a,b, 2, 22k) and ς(a',b', 2, 2 2k), are diffeomorphic as abstract manifolds. Let J and K be (not necessarily connected or spherical) 2-dimensional closed oriented submanifolds in S4. Suppose that J is obtained from K by a single ribbon-move, which is a local-move on 2-dimensional submanifolds contained in S4. Let k be an integer ≥ 2. We prove the following: The (4k + 2)-submanifold JS - HopfS - k S S4k+4 is obtained from KS - HopfS - k by a single (2k + 1, 2k + 2)-pass-move, which is a local-move on (4k + 2)-dimensional submanifolds contained in S4k+4.",
keywords = "branched cyclic covering spaces, Local-moves on 1-knots, local-moves on high-dimensional knots, products of knots, q) -pass-move on high-dimensional links, Seifert hypersurfaces, Seifert matrices, the (p, the crossing-change on 1-links, the pass-move on 1-links, the (p, q) -pass-move on high-dimensional links",
author = "Kauffman, {Louis H.} and Eiji Ogasa",
note = "Kauffman's work was supported by the Laboratory of Topology and Dynamics, Novosibirsk State University (Contract No. 14.Y26.31.0025 with the Ministry of Education and Science of the Russian Federation). Publisher Copyright: {\textcopyright} 2021 World Scientific Publishing Company.",
year = "2021",
month = sep,
day = "1",
doi = "10.1142/S021821652140006X",
language = "English",
volume = "30",
journal = "Journal of Knot Theory and its Ramifications",
issn = "0218-2165",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "10",

}

RIS

TY - JOUR

T1 - Local-moves on knots and products of knots II

AU - Kauffman, Louis H.

AU - Ogasa, Eiji

N1 - Kauffman's work was supported by the Laboratory of Topology and Dynamics, Novosibirsk State University (Contract No. 14.Y26.31.0025 with the Ministry of Education and Science of the Russian Federation). Publisher Copyright: © 2021 World Scientific Publishing Company.

PY - 2021/9/1

Y1 - 2021/9/1

N2 - We use the terms, knot product and local-move, as defined in the text of this paper. Let n be an integer 3. Let n be the set of simple spherical n-knots in Sn+2. Let m be an integer 4. We prove that the map j: 2m →2m+4 is bijective, where j(K) = KS - Hopf, and Hopf denotes the Hopf link. Let J and K be 1-links in S3. Suppose that J is obtained from K by a single pass-move, which is a local-move on 1-links. Let k be a positive integer. Let P S - QS - k denote the knot product P S - Q S - ⋯ S - Qk. We prove the following: The (4k + 1)-dimensional submanifold JS - HopfS - k S S4k+3 is obtained from KS - HopfS - k by a single (2k+1, 2k+1)-pass-move, which is a local-move on (4k + 1)-submanifolds contained in S4k+3. See the body of this paper for the definitions of all local-moves in this abstract. We prove the following: Let a,b,a',b', and k be positive integers. If the (a,b) torus link is pass-move-equivalent to the (a',b') torus link, then the Brieskorn manifolds, ς(a,b, 2, 22k) and ς(a',b', 2, 2 2k), are diffeomorphic as abstract manifolds. Let J and K be (not necessarily connected or spherical) 2-dimensional closed oriented submanifolds in S4. Suppose that J is obtained from K by a single ribbon-move, which is a local-move on 2-dimensional submanifolds contained in S4. Let k be an integer ≥ 2. We prove the following: The (4k + 2)-submanifold JS - HopfS - k S S4k+4 is obtained from KS - HopfS - k by a single (2k + 1, 2k + 2)-pass-move, which is a local-move on (4k + 2)-dimensional submanifolds contained in S4k+4.

AB - We use the terms, knot product and local-move, as defined in the text of this paper. Let n be an integer 3. Let n be the set of simple spherical n-knots in Sn+2. Let m be an integer 4. We prove that the map j: 2m →2m+4 is bijective, where j(K) = KS - Hopf, and Hopf denotes the Hopf link. Let J and K be 1-links in S3. Suppose that J is obtained from K by a single pass-move, which is a local-move on 1-links. Let k be a positive integer. Let P S - QS - k denote the knot product P S - Q S - ⋯ S - Qk. We prove the following: The (4k + 1)-dimensional submanifold JS - HopfS - k S S4k+3 is obtained from KS - HopfS - k by a single (2k+1, 2k+1)-pass-move, which is a local-move on (4k + 1)-submanifolds contained in S4k+3. See the body of this paper for the definitions of all local-moves in this abstract. We prove the following: Let a,b,a',b', and k be positive integers. If the (a,b) torus link is pass-move-equivalent to the (a',b') torus link, then the Brieskorn manifolds, ς(a,b, 2, 22k) and ς(a',b', 2, 2 2k), are diffeomorphic as abstract manifolds. Let J and K be (not necessarily connected or spherical) 2-dimensional closed oriented submanifolds in S4. Suppose that J is obtained from K by a single ribbon-move, which is a local-move on 2-dimensional submanifolds contained in S4. Let k be an integer ≥ 2. We prove the following: The (4k + 2)-submanifold JS - HopfS - k S S4k+4 is obtained from KS - HopfS - k by a single (2k + 1, 2k + 2)-pass-move, which is a local-move on (4k + 2)-dimensional submanifolds contained in S4k+4.

KW - branched cyclic covering spaces

KW - Local-moves on 1-knots

KW - local-moves on high-dimensional knots

KW - products of knots

KW - q) -pass-move on high-dimensional links

KW - Seifert hypersurfaces

KW - Seifert matrices

KW - the (p

KW - the crossing-change on 1-links

KW - the pass-move on 1-links

KW - the (p, q) -pass-move on high-dimensional links

UR - http://www.scopus.com/inward/record.url?scp=85122311182&partnerID=8YFLogxK

U2 - 10.1142/S021821652140006X

DO - 10.1142/S021821652140006X

M3 - Article

AN - SCOPUS:85122311182

VL - 30

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

SN - 0218-2165

IS - 10

M1 - 2140006

ER -

ID: 35262240