尖点三维流形的Pachner移动和收缩的界
Bounds on Pachner moves and systoles of cusped 3-manifolds
摘要：
尖点完备双曲$3$ -流形$M$的任意两个几何理想三角剖分通过拓扑三角剖分的Pachner移动序列联系起来。我们给出了这个序列的长度上的限制，在四面体的总数和一个下界上的二面角。这导致了一个天真但有效的算法来检查两个双曲结是否等价，给出了它们的互补的几何理想三角剖分。给定$M$的一个几何理想三角剖分，我们还给出了$M$收缩长度的一个由四面体个数表示的下界和二面角的一个下界.
英文摘要：
Any two geometric ideal triangulations of a cusped complete hyperbolic $3$-manifold $M$ are related by a sequence of Pachner moves through topological triangulations. We give a bound on the length of this sequence in terms of the total number of tetrahedra and a lower bound on dihedral angles. This leads to a naive but effective algorithm to check if two hyperbolic knots are equivalent, given geometric ideal triangulations of their complements. Given a geometric ideal triangulation of $M$, we also give a lower bound on the systole length of $M$ in terms of the number of tetrahedra and a lower bound on dihedral angles.
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。
