Estimating Matveev's complexity via crystallization theory
The definition of Matveev's complexity \(c(M^3)\) of a \(3\)--dimensional manifold \(M^3\) is based on the existence of a \textit{simple spine} for \(M^3\) [\textit{S. V. Matveev}, Acta Appl. Math. 19, No.~2, 101--130 (1990; Zbl 0724.57012)]. In the paper under discussion the author studies Matveev's complexity by making use of another combinatorial description of \(M^3\), the so called crystallization. This allows to improve the known estimates of \(c(M^3)\) for manifolds given as a \(2\)-fold or \(3\)-fold simple branched covering over links in \(S^3\) as well as for \(3\)-manifolds given by Dehn surgery on a framed link in \(S^3\).
scientific article; zbMATH DE number 5130426
scientific article