Matveev, S. V. Complexity theory of three-dimensional manifolds. (English) Zbl 0724.57012 Acta Appl. Math. 19, No. 2, 101-130 (1990). Each compact 3-manifold has a spine which is almost special - a polyhedron in which the link of each vertex embeds in the 1-skeleton of the 3-simplex. A complexity is defined for 3-manifolds by taking the minimum over all almost special spines of the number of vertices for which the link is the entire 1-skeleton of the 3-simplex. Some properties of this complexity are established: (A) there are only finitely many 3- manifolds with a given complexity, (B) complexity is additive over connected sums, and (C) cutting an irreducible, \(\partial\)-irreducible 3- manifold along an incompressible, and \(\partial\)-incompressible surface cannot increase complexity. A list of all 3-manifolds with complexity \(\leq 6\) is given. Reviewer: J.Hempel (Houston) Cited in 25 ReviewsCited in 42 Documents MSC: 57N10 Topology of general \(3\)-manifolds (MSC2010) 57Nxx Topological manifolds Keywords:compact 3-manifold; spine; complexity PDF BibTeX XML Cite \textit{S. V. Matveev}, Acta Appl. Math. 19, No. 2, 101--130 (1990; Zbl 0724.57012) OpenURL Online Encyclopedia of Integer Sequences: The number of (tame) knots and links with Matveev complexity n for closed manifolds, given by Heard in the form of a surgery description when the underlying space is not S^3.