Nonconstructible Simplicial Balls and a Way of Testing Constructibility

Constructibility of simplicial complexes is a notion weaker than shellability. It is known that shellable pseudomanifolds are homeomorphic to balls or spheres but simplicial complexes homeomorphic to balls or spheres need not be shellable in general. Constructible pseudomanifolds are also homeomorphic to balls or spheres, but the existence of nonconstructible balls was not known. In this paper we study the constructibility of some nonshellable balls and show that some of them are not constructible, either. Moreover, we give a necessary and sufficient condition for the constructibility of three-dimensional simplicial balls, whose vertices are all on the boundary. Received September 29, 1997, and in revised form August 3, 1998 and August 11, 1998.