Constructing \(n\)-manifolds from spines (Q1272781)

Let \((H,\zeta)\) be an \((n-1)\)-dimensional complex. A pluri-bijoin over \((H,\zeta)\) is an \(n\)-dimensional coloured complex \((K,\xi)\) such that: (a) \(| K| \) is a quasi-manifold, (b) there is a colour \(c\in C\) such that \((H,\zeta)\) is colour isomorphic to \((K(\)ĉ),\(\xi')\). If \(\xi^{-1}(c)\) has cardinality \(h\) then \((K,\xi)\) is an \(h\)-bijoin over \((H,\zeta)\). If \(h=1\) then \((K,\xi)\) is a bijoin over \((H,\zeta)\). The author extends to the non-orientable case some algorithms for constructing all orientable pluri-bijoins over any given coloured pseudo-complex \(H\) of dimension \(n-1\). There are obtained all orientable or non-orientable pluri-bijoins over \(H\) and the corresponding algorithm reduces to the known algorithm in the orientable case. It is given a characterization of the pluri-bijoins \(K\) over \(H\), triangulating closed (orientable or nonorientable) \(3\)-manifolds.