论文标题
将3个manifold三角剖分与基本移动的单峰序列连接
Connecting 3-manifold triangulations with unimodal sequences of elementary moves
论文作者
论文摘要
计算3个manifold拓扑结构的关键结果是，相同3个manifold的任何两个三角剖分都通过有限的Bistellar翻转序列连接，也称为Pachner Moves。该结果的一个局限性是对该序列的结构知之甚少。了解该结构可以帮助证明和算法。在此激励的情况下，我们考虑了它们分为两个部分的意义上是“单峰”的序列：首先是单调增加三角测量大小的序列；其次，单调降低大小的序列。我们证明，同一3个序列的任何两个单vertex三角剖分，每个三角形至少两个四面体，都通过2-3和2-0的单峰序列连接。我们还研究了单峰序列的实际实用性。具体而言，我们实现了一种算法来查找此类序列，并使用此算法来执行一些详细的计算实验。
A key result in computational 3-manifold topology is that any two triangulations of the same 3-manifold are connected by a finite sequence of bistellar flips, also known as Pachner moves. One limitation of this result is that little is known about the structure of this sequence; knowing more about the structure could help both proofs and algorithms. Motivated by this, we consider sequences of moves that are "unimodal" in the sense that they break up into two parts: first, a sequence that monotonically increases the size of the triangulation; and second, a sequence that monotonically decreases the size. We prove that any two one-vertex triangulations of the same 3-manifold, each with at least two tetrahedra, are connected by a unimodal sequence of 2-3 and 2-0 moves. We also study the practical utility of unimodal sequences; specifically, we implement an algorithm to find such sequences, and use this algorithm to perform some detailed computational experiments.
