翻訳と辞書
Words near each other
・ "O" Is for Outlaw
・ "O"-Jung.Ban.Hap.
・ "Ode-to-Napoleon" hexachord
・ "Oh Yeah!" Live
・ "Our Contemporary" regional art exhibition (Leningrad, 1975)
・ "P" Is for Peril
・ "Pimpernel" Smith
・ "Polish death camp" controversy
・ "Pro knigi" ("About books")
・ "Prosopa" Greek Television Awards
・ "Pussy Cats" Starring the Walkmen
・ "Q" Is for Quarry
・ "R" Is for Ricochet
・ "R" The King (2016 film)
・ "Rags" Ragland
・ ! (album)
・ ! (disambiguation)
・ !!
・ !!!
・ !!! (album)
・ !!Destroy-Oh-Boy!!
・ !Action Pact!
・ !Arriba! La Pachanga
・ !Hero
・ !Hero (album)
・ !Kung language
・ !Oka Tokat
・ !PAUS3
・ !T.O.O.H.!
・ !Women Art Revolution


Dictionary Lists
翻訳と辞書 辞書検索 [ 開発暫定版 ]
スポンサード リンク

satellite knot : ウィキペディア英語版
satellite knot
In the mathematical theory of knots, a satellite knot is a knot that contains an incompressible, non boundary-parallel torus in its complement.〔Colin Adams, ''The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots'', (2001), ISBN 0-7167-4219-5〕 Every knot is either hyperbolic, a torus, or a satellite knot. The class of satellite knots include composite knots, cable knots and Whitehead doubles. (''See'' Basic families, below for definitions of the last two classes.) A satellite ''link'' is one that orbits a companion knot ''K'' in the sense that it lies inside a regular neighborhood of the companion.

A satellite knot K can be picturesquely described as follows: start by taking a nontrivial knot K' lying inside an unknotted solid torus V. Here "nontrivial" means that the knot K' is not allowed to sit inside of a 3-ball in V and K' is not allowed to be isotopic to the central core curve of the solid torus. Then tie up the solid torus into a nontrivial knot.
This means there is a non-trivial embedding f\colon V \to S^3 and K=f(K'). The central core curve of the solid torus V is sent to a knot H, which is called the "companion knot" and is thought of as the planet around which the "satellite knot" K orbits.The construction ensures that f(\partial V) is a non-boundary parallel incompressible torus in the complement of K. Composite knots contain a certain kind of incompressible torus called a swallow-follow torus, which can be visualized as swallowing one summand and following another summand.
Since V is an unknotted solid torus, S^3 \setminus V is a tubular neighbourhood of an unknot J. The 2-component link K' \cup J together with the embedding f is called the ''pattern'' associated to the satellite operation.
A convention: people usually demand that the embedding f \colon V \to S^3 is ''untwisted'' in the sense that f must send the standard longitude of V to the standard longitude of f(V). Said another way, given two disjoint curves c_1,c_2 \subset V, f must preserve their linking numbers i.e.: lk(f(c_1),f(c_2))=lk(c_1,c_2).
==Basic families==

When K' \subset \partial V is a torus knot, then K is called a ''cable knot.'' Examples 3 and 4 are cable knots.
If K' is a non-trivial knot in S^3 and if a compressing disc for V intersects K' in precisely one point, then K is called a ''connect-sum.'' Another way to say this is that the pattern K' \cup J is the connect-sum of a non-trivial knot K' with a Hopf link.
If the link K' \cup J is the Whitehead link, K is called a ''Whitehead double.'' If f is untwisted, K is called an untwisted Whitehead double.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「satellite knot」の詳細全文を読む



スポンサード リンク
翻訳と辞書 : 翻訳のためのインターネットリソース

Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.