Matveev, S. V. Generalized graph manifolds and their effective recognition. (English. Russian original) Zbl 0967.57019 Sb. Math. 189, No. 10, 1517-1531 (1998); translation from Mat. Sb. 189, No. 10, 89-104 (1998). Summary: By a generalized graph manifold the author means a 3-dimensional manifold obtained by glueing together elementary blocks, each of which is either a Seifert manifold or contains no essential tori or annuli. It follows from the well-known toric decomposition theorem that any compact 3-dimensional manifold the boundary of which being either empty or consisting of tori has a canonical representation as a generalized graph manifold. The author gives a simple and short independent proof of the existence of a canonical representation, and describes a partial algorithm for its construction. He also gives a simple criterion for the hyperbolicity of blocks that are not Seifert manifolds. MSC: 57N10 Topology of general \(3\)-manifolds (MSC2010) 52B70 Polyhedral manifolds PDFBibTeX XMLCite \textit{S. V. Matveev}, Sb. Math. 189, No. 10, 1517--1531 (1998; Zbl 0967.57019); translation from Mat. Sb. 189, No. 10, 89--104 (1998) Full Text: DOI