Upper bounds for the complexity of torus knot complements (Q2859559)

The definition of \textit{Matveev complexity} \(c(M)\) of a compact 3-manifold with nonempty boundary \(M\) is based on the existence of an almost simple spine for \(M\): see [\textit{S. V. Matveev}, Acta Appl. Math. 19, No. 2, 101--130 (1990; Zbl 0724.57012)].NEWLINENEWLINEThe complexity of a given 3-manifold is generally hard to compute from the theoretical point of view, leaving aside the concrete enumeration of its spines: see, for example, [\textit{S. Matveev}, Algorithmic topology and classification of 3-manifolds. Berlin: Springer (2003; Zbl 1048.57001)] and [\textit{W. Jaco} et al., Algebr. Geom. Topol. 11, No. 3, 1257--1265 (2011; Zbl 1229.57010)], together with their references.NEWLINENEWLINE\smallskipNEWLINENEWLINEIn the paper under discussion the authors establish an upper bound for the Matveev complexity of any Seifert fibered 3-manifold with nonempty boundary \(M\), by realizing \(M\) as an assembly of several copies of five particular \textit{building blocks}, whose skeleta contain a known number of true vertices. As a consequence, they obtain potentially sharp bounds on the Matveev complexity of torus knot complements.