Plane number of links

Shosaku Matsuzaki

doi:10.1142/S021821651550039X

Plane number of links

Shosaku Matsuzaki^*

^*Corresponding author for this work

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

2 Citations (Scopus)

Abstract

Let L = L₁ ∪ L₂ ∪ ⋯ ∪ Ln be a link in ℝ³ such that Li is a trivial link for each i, 1 ≤ i ≤ n. Let P₁, P₂,...,P n be mutually distinct flat planes in ℝ³ such that no two of them are parallel. Then there is a link L′ = L{1}′ ∪ L{2}′ ∪ \cdots ∪ L{n}′ in ℝ³ such that L is ambient isotopic to L′ and L{i}′ \subset P{i} for each i, 1 ≤ i ≤ n.

Original language	English
Article number	1550039
Journal	Journal of Knot Theory and its Ramifications
Volume	24
Issue number	7
DOIs	https://doi.org/10.1142/S021821651550039X
Publication status	Published - 2015 Jun 3

Keywords

Brunnian link
Link
plane number
plane-arrangement

ASJC Scopus subject areas

Algebra and Number Theory

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10.1142/S021821651550039X

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title = "Plane number of links",

abstract = "Let L = L1 ∪ L2 ∪ ⋯ ∪ Ln be a link in ℝ3 such that Li is a trivial link for each i, 1 ≤ i ≤ n. Let P1, P2,...,P n be mutually distinct flat planes in ℝ3 such that no two of them are parallel. Then there is a link L′ = L{1}′ ∪ L{2}′ ∪ \cdots ∪ L{n}′ in ℝ3 such that L is ambient isotopic to L′ and L{i}′ \subset P{i} for each i, 1 ≤ i ≤ n.",

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author = "Shosaku Matsuzaki",

year = "2015",

month = jun,

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AU - Matsuzaki, Shosaku

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N2 - Let L = L1 ∪ L2 ∪ ⋯ ∪ Ln be a link in ℝ3 such that Li is a trivial link for each i, 1 ≤ i ≤ n. Let P1, P2,...,P n be mutually distinct flat planes in ℝ3 such that no two of them are parallel. Then there is a link L′ = L{1}′ ∪ L{2}′ ∪ \cdots ∪ L{n}′ in ℝ3 such that L is ambient isotopic to L′ and L{i}′ \subset P{i} for each i, 1 ≤ i ≤ n.

AB - Let L = L1 ∪ L2 ∪ ⋯ ∪ Ln be a link in ℝ3 such that Li is a trivial link for each i, 1 ≤ i ≤ n. Let P1, P2,...,P n be mutually distinct flat planes in ℝ3 such that no two of them are parallel. Then there is a link L′ = L{1}′ ∪ L{2}′ ∪ \cdots ∪ L{n}′ in ℝ3 such that L is ambient isotopic to L′ and L{i}′ \subset P{i} for each i, 1 ≤ i ≤ n.

KW - Brunnian link

KW - Link

KW - plane number

KW - plane-arrangement

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JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

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ER -

Plane number of links

Abstract

Keywords

ASJC Scopus subject areas

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