Simplicial Manifolds, Bistellar Flips and a 16-Vertex Triangulation of the Poincaré Homology 3-Sphere

Abstract

We present a computer program based on bistellar operations that provides a useful tool for the construction of simplicial manifolds with few vertices. As an example, we obtain a 16-vertex triangulation of the Poincaré homology 3-sphere; we construct an infinite series of non-PL. d-dimensional spheres with d + 13 vertices for d ≥ 5; and we show that if a d-manifold, with d ≥ 5, admits any triangulation on n vertices, it admits a noncombinatorial triangu lation on n + 12 vertices.