\(\mathcal F\)-manifolds and dual cellular functions (Q1179833)

The aim of the paper is to study the topological structure of a special type of polyhedra, called \(F\)-manifolds, which generalize the concept of homology manifold. Under additional conditions of (co)connectedness, it is proved that (weak) dual cellular maps preserve the \(F\)-manifold structure. In particular, these morphisms are shown to be the acyclic (resp. cellular transversal) maps in the category of homology (resp. piecewise linear) manifolds [see also \textit{M. M. Cohen}, Ann. Math. (2) 85, 218--245 (1967; Zbl 0147.42602)].