- Experiment. Math.
- Volume 9, Issue 2 (2000), 275-289.
Simplicial manifolds, bistellar flips and a 16-vertex triangulation of the Poincaré homology 3-sphere
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.
Experiment. Math., Volume 9, Issue 2 (2000), 275-289.
First available in Project Euclid: 22 February 2003
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57Q15: Triangulating manifolds
Secondary: 57-04: Explicit machine computation and programs (not the theory of computation or programming) 57M15: Relations with graph theory [See also 05Cxx] 57Q25: Comparison of PL-structures: classification, Hauptvermutung
Björner, Anders; Lutz, Frank H. Simplicial manifolds, bistellar flips and a 16-vertex triangulation of the Poincaré homology 3-sphere. Experiment. Math. 9 (2000), no. 2, 275--289. https://projecteuclid.org/euclid.em/1045952351