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

Björner, Anders; Lutz, Frank H.

Experiment. Math., Tome 9 (2000) no. 3, p. 275-289 / Harvested from Project Euclid

Résumé

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.

Publié le : 2000-05-14
Classification: 57Q15, 57-04, 57M15, 57Q25

@article{1045952351,
     author = {Bj\"orner, Anders and Lutz, Frank H.},
     title = {Simplicial manifolds, bistellar flips and a 16-vertex triangulation of the Poincar\'e homology 3-sphere},
     journal = {Experiment. Math.},
     volume = {9},
     number = {3},
     year = {2000},
     pages = { 275-289},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1045952351}
}

Björner, Anders; Lutz, Frank H. Simplicial manifolds, bistellar flips and a 16-vertex triangulation of the Poincaré homology 3-sphere. Experiment. Math., Tome 9 (2000) no. 3, pp.  275-289. http://gdmltest.u-ga.fr/item/1045952351/