Connecting 3-manifold triangulations with unimodal sequences of elementary moves
Benjamin A. Burton, Alexander He
计算三流形拓扑的一个关键结果是,同一三流形的任何两个三角测量都通过有限序列的双星翻转连接,也称为Pachner移动。 这个结果的一个限制是,对于这个序列的结构知之甚少;更多地了解结构可以帮助证明和算法。 受此激励,我们考虑的是“单模态”的动数序列,因为它们分为两部分:第一,单调地增加三角测量大小的序列;第二,单调地减小大小。 我们证明,任何两个相同的三流形的单向三角测量,每个三流形至少有两个四面体,通过2-3和2-0移动的单模态序列连接。 我们还研究了单模态序列的实际效用;具体地说,我们实现了一种算法来找到这样的序列,并使用这种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 monoton...
