Universal coverings of PL-manifolds via coloured graphs
The authors use the representation of piecewise linear manifolds by means of edge-coloured graphs [see, e.g., \textit{M. Ferri, C. Gagliardi} and \textit{L. Grasselli}, Aequationes Math. 31, 121-141 (1986; Zbl 0623.57012)]. This approach together with some results concerning universal covering maps allow one to construct an infinite ball complex \(P(n)\), \(n>1\), such that every orientable PL \(n\)-manifold is a quotient of the polyhedron underlying \(P(n)\) under the action of a finite index subgroup of a certain Fuchsian group. Then the authors introduce a combinatorial invariant of a closed connected PL manifold \(M\), called the type of \(M\), and prove some results about the calculation of this invariant for surfaces and manifolds of dimension 3.
representation of piecewise linear manifolds by edge-coloured graphs
scientific article; zbMATH DE number 85812