Many Triangulated 3-Spheres
度量几何
2007-05-23 v2 组合数学
几何拓扑
摘要
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.
引用
@article{arxiv.math/0212004,
title = {Many Triangulated 3-Spheres},
author = {Julian Pfeifle and Günter M. Ziegler},
journal= {arXiv preprint arXiv:math/0212004},
year = {2007}
}
备注
9 pages, 4 figures; Incorporated referee's comments; to appear in Math. Annalen