Experimental Mathematics

Simplicial manifolds, bistellar flips and a 16-vertex triangulation of the Poincaré homology 3-sphere

Anders Björner and Frank H. Lutz

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.

Article information

Source
Experiment. Math., Volume 9, Issue 2 (2000), 275-289.

Dates
First available in Project Euclid: 22 February 2003

Permanent link to this document
https://projecteuclid.org/euclid.em/1045952351

Mathematical Reviews number (MathSciNet)
MR1780212

Zentralblatt MATH identifier
1101.57306

Subjects
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

Citation

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


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