Talk:Graph manifold

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It seems unlikely that the name "graph manifolds" comes from the JSJ decomposition, because JSJ decomposition was invented in the mid-70's whereas Waldhausen's original article (,,Eine Klasse von 3-dimensionalen Mannigfaltigkeiten") was published in 1967, and uses this very denomination (,,Graphenmannigfaltigkeit").

The convenient representation by graphs is already in Waldhausen's article (9 ,,Klassification der ,meisten' reduzierten Graphenmannigfatigkeiten"). According to Hatcher, this article is in fact very close to the discovery of JSJ-decomposition. — Preceding unsigned comment added by 140.77.128.41 (talk) 15:44, 5 July 2006 (UTC)[reply]

Needs much work, above all a definition of its subject

This article defines a graph manifold as follows:

"In topology, a graph manifold (in German: Graphenmannigfaltigkeit) is a 3-manifold which is obtained by gluing some circle bundles."

This is so very lacking detail as to be more likely to annoy than inform any reader who came here to learn what a graph manifold is.

I hope someone knowledgeable about this subject can provide at minimum a complete and clear, uncomplicated definition of what a graph manifold is.

I recall Bill Thurston once telling me that a graph manifold is a 3-manifold whose JSJ decomposition consists entirely of Seifert-fibred pieces. If that is accurate, then it seems like an essential defining quality of graph manifolds that really should be mentioned in the article.

I think also a lot of people, myself included, would also like to know how the name "graph manifold" got chosen for this concept.

The second paragraph contains an actual definition in technical terms. An explanation for the name is given at the end of the first paragraph. jraimbau (talk) 07:38, 12 February 2025 (UTC)[reply]