| 翻訳と辞書 |
Slam-dunk
In mathematics, particularly low-dimensional topology, the slam-dunk is a particular modification of a given surgery diagram in the 3-sphere for a 3-manifold. The name, but not the move, is due to Tim Cochran. Let ''K'' be a component of the link in the diagram and ''J'' be a component that circles ''K'' as a meridian. Suppose ''K'' has integer coefficient ''n'' and ''J'' has coefficient a rational number ''r''. Then we can obtain a new diagram by deleting ''J'' and changing the coefficient of ''K'' to ''n-1/r''. This is the slam-dunk.
The name of the move is suggested by the proof that these diagrams give the same 3-manifold. First, do the surgery on ''K'', replacing a tubular neighborhood of ''K'' by another solid torus ''T'' according to the surgery coefficient ''n''. Since ''J'' is a meridian, it can be pushed, or "slam dunked", into ''T''. Since ''n'' is an integer, ''J'' intersects the meridian of ''T'' once, and so ''J'' must be isotopic to a longitude of ''T''. Thus when we now do surgery on ''J'', we can think of it as replacing ''T'' by another solid torus. This replacement, as shown by a simple calculation, is given by coefficient ''n - 1/r''.
The inverse of the slam-dunk can be used to change any rational surgery diagram into an integer one, i.e. a surgery diagram on a framed link.
==References==
* Robert Gompf and Andras Stipsicz, ''4-Manifolds and Kirby Calculus'', (1999) (Volume 20 in ''Graduate Studies in Mathematics''), American Mathematical Society, Providence, RI ISBN 0-8218-0994-6
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「Slam-dunk」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.
|
|