Many triangulated 3-spheres
Julian Pfeifle and Günter M. Ziegler – 2004
We construct 2^{\Omega(n^{5/4})} combinatorial types of triangulated 3-spheres on n vertices. Since by a result of Goodman and Pollack (1986) there are no more than 2^{O(n log n)} combinatorial types of simplicial 4-polytopes, this proves that asymptotically, there are far more combinatorial types of triangulated 3-spheres than of simplicial 4-polytopes on n vertices. This complements results of Kalai (1988), who had proved a similar statement about d-spheres and (d+1)-polytopes for fixed d >= 4.
Titel
Many triangulated 3-spheres
Verfasser
Julian Pfeifle and Günter M. Ziegler
Datum
2004
Quelle/n
Erschienen in
Mathematische Annalen, volume 330, pages 829-837
Art
Text