Polytopal Bier Spheres and Kantorovich–Rubinstein Polytopes of Weighted Cycles
Polytopal Bier Spheres and Kantorovich–Rubinstein Polytopes of Weighted Cycles
复制标题
多胞体啤酒球和加权循环的 Kantorovich-Rubinstein 多胞体
DOI：
10.1007/s00454-019-00151-5
复制
发表时间：
2018
影响因子：
0.8
通讯作者：
R. Živaljević
中科院分区：
文献类型：
--
作者：
Filip D. Jevtic;Marinko Timotijević;R. Živaljević
决定一个给定的球面三角剖分是否可以实现为一个单纯凸多面体的边界球面的问题被称为“单纯斯坦尼兹问题”。通过一个间接的和非建设性的论证，我们知道绝大多数比尔球是非多面体的。与此相反，我们证明了与阈值单纯复形相关的Bier球都是多面体。此外，我们证明了所有的Bier球是星形的。我们还建立了一个连接的比尔领域和Kantorovich-Rubinstein多面体之间的边界领域的KR-多面体相关联的多边形链接（加权循环）是同构的比尔领域的相关单纯复杂的“短集”。
The problem of deciding if a given triangulation of a sphere can be realized as the boundary sphere of a simplicial, convex polytope is known as the ‘Simplicial Steinitz problem’. It is known by an indirect and non-constructive argument that a vast majority of Bier spheres are non-polytopal. Contrary to that, we demonstrate that the Bier spheres associated to threshold simplicial complexes are all polytopal. Moreover, we show that all Bier spheres are starshaped. We also establish a connection between Bier spheres and Kantorovich–Rubinstein polytopes by showing that the boundary sphere of the KR-polytope associated to a polygonal linkage (weighted cycle) is isomorphic to the Bier sphere of the associated simplicial complex of “short sets”.
三角流形数量的 Cheeger 型指数界
DOI：
10.4171/aihpd/85
发表时间：
2020
期刊：
Annales de l’Institut Henri Poincaré D
影响因子：
--
作者：
Adiprasito, Karim;Benedetti, Bruno
通讯作者：
Benedetti, Bruno