Discrete & Computational Geometry Vol.22 No.2 (1999), 223-230.
Nonconstructible Simplicial Balls and a Way of Testing Constructibility.
by Masahiro Hachimori
Abstract
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.