# Talk:Manifold decomposition

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Field:  Topology

At some point, somebody changed the entry for sutured manifold hierarchy to one for disc decompositions, which are a special kind of sutured manifold hierarchy. I'm not sure why this was done. It's good to have them both. Disc decompositions are used frequently, but the general concept shouldn't be deleted altogether. --C S 07:55, 10 October 2005 (UTC)

One thing about this page that strikes me again and again every time I look at it is how cumbersome it is. It was a nice initial idea to have a general decomposition page...but there's no real nice way to make a table that encompasses the really different kinds of decompositions there are. For example, in hierarchies, one has a sequence of cuttings, and at the end one might have nice pieces like balls or sutured balls or whatever. But saying the "pieces" of the decomposition are balls has quite a different meaning here than saying the pieces of a triangulation are simplices. I could go on and on. But I won't :-) --C S 08:02, 10 October 2005 (UTC)

I have removed the higher dimensions: there is no general definition of "prime manifold". In fact, a definition would only work in the topological category (because of the proved Poincaré conjecures), and not in the smooth category (in dimension 4 there may be no prime manifolds at all, not even ${\displaystyle S^{4}}$). It is misleading to simply say that "it works in all dimensions". Ylebru (talk) 09:42, 8 January 2008 (UTC)