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Manifold decomposition : ウィキペディア英語版
Manifold decomposition

In topology, a branch of mathematics, a manifold ''M'' may be decomposed or split by writing ''M'' as a combination of smaller pieces. When doing so, one must specify both what those pieces are and how they are put together to form ''M''.
Manifold decomposition works in two directions: one can start with the smaller pieces and build up a manifold, or start with a large manifold and decompose it. The latter has proven a very useful way to study manifolds: without tools like decomposition, it is sometimes very hard to understand a manifold. In particular, it has been useful in attempts to classify 3-manifolds and also in proving the higher-dimensional Poincaré conjecture.
The table below is a summary of the various manifold-decomposition techniques. The column labeled "''M''" indicates what kind of manifold can be decomposed; the column labeled "How it is decomposed" indicates how, starting with a manifold, one can decompose it into smaller pieces; the column labeled "The pieces" indicates what the pieces can be; and the column labeled "How they are combined" indicates how the smaller pieces are combined to make the large manifold.

==See also==

* Surgery theory

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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