A structure theorem for pseudomanifolds

We introduce the notion of primitive pseudo-manifolds and prove that all pseudo-manifolds (without boundary) are built out of the primitive ones by a canonical procedure. This theory is used to explicitly determine and count all the pseudo-manifolds of dimension d greater than or equal to 1 on at most d + 4 vertices. As a consequence, it turns out that their geometric realisations are either spheres or iterated suspensions of the real projective plane. (C) 1998 Elsevier Science B.V. All rights reserved.