随机单同伦理论
Random Simple-Homotopy Theory
摘要：
我们实现了一个算法RSHT（随机简单同伦）来研究单纯复形的简单同伦类型，特别关注可收缩空间和高维复形中的子结构。该算法结合了初等单纯折叠和纯初等展开。对于d < 7的三角剖分d流形，我们证明了RSHT约化为（随机）bistellar翻转。在许多例子中，我们测试RSHT，我们描述了一个明确的15顶点三角剖分的鲍鱼，更一般地说，（14k+1）顶点三角剖分的Bing的房子与k个房间，这一切都可以变形到一个点，只使用六个纯基本扩展。
英文摘要：
We implement an algorithm RSHT (Random Simple-Homotopy) to study the simple-homotopy types of simplicial complexes, with a particular focus on contractible spaces and on finding substructures in higher-dimensional complexes. The algorithm combines elementary simplicial collapses with pure elementary expansions. For triangulated d-manifolds with d < 7, we show that RSHT reduces to (random) bistellar flips. Among the many examples on which we test RSHT, we describe an explicit 15-vertex triangulation of the Abalone, and more generally, (14k+1)-vertex triangulations of Bing's houses with k rooms, which all can be deformed to a point using only six pure elementary expansions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
