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editIt 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)