Chromatic Homotopy Theory
《Chromatic Homotopy Theory》 · 第 366–367 页 · Section 11.5.1，torus decomposition、minimal 的定义及 Theorem 11.5.1
Let \(M\) be an orientable irreducible and \(\partial\)-irreducible compact 3-manifold with (possibly empty) boundary consisting of tori. […] Let \(S=T_1\sqcup\cdots\sqcup T_k\) be a set of disjoint essential tori \(T_i\subset\operatorname{int}(M)\). We say that \(S\) is a torus decomposition of \(M\) if it decomposes \(M\) into blocks that are either: torus (semi-)bundles, Seifert manifolds, or simple manifolds. A torus decomposition is minimal if no proper subset of \(S\) is a torus decomposition. […] Such a minimal decomposition is called the canonical torus decomposition or the JSJ decomposition of \(M\).