A class of 4-pseudomanifolds similar to the lens spaces (Q1095454)

A family of 4-dimensional pseudomanifolds (lens-like spaces) is defined and studied by means of edge-coloured graphs. Its main interest consists in the similarities with the 3-dimensional lens spaces L(p,q). The ``normal'' graph-theoretical representation of the latter [see the author and \textit{L. Grasselli}, Boll. Unione Mat. Ital., VI. Ser., A 1, 359-366 (1982; Zbl 0502.57007)] has suggested the form of the graphs, which depend on three integers p, \(q_ 1\), \(q_ 2\). The spaces are nonorientable, and one of them is \(RP^ 4\), which is also the only manifold of the family. Sufficient conditions for the homeomorphism of members of the family are given, which resemble the classical (also necessary) conditions in dimension 3. The singularity types, the fundamental groups, and bounds for the genera in the sense of \textit{C. Gagliardi} [Proc. Am. Math. Soc. 81, 473-481 (1981; Zbl 0467.57004)] are computed for the lens-like spaces.