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 $d\geq 5$; and we show that if a d-manifold, with $d\ge 5$, admits any triangulation on n vertices, it admits a noncombinatorial triangulation on n+12 vertices.
Citation
Anders Björner. Frank H. Lutz. "Simplicial manifolds, bistellar flips and a 16-vertex triangulation of the Poincaré homology 3-sphere." Experiment. Math. 9 (2) 275 - 289, 2000.
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