论文标题
Pachner移动和收缩的界限3- manifolds
Bounds on Pachner moves and systoles of cusped 3-manifolds
论文作者
论文摘要
cused完整双曲线$ 3 $ manifold $ m $的任何两个几何理想三角剖分都与一系列Pachner通过拓扑三角剖分有关。我们根据四面体的总数和二面角的下限给出了该序列的长度。这会导致一种天真但有效的算法检查其补充的几何理想三角剖分，是否两个双曲线结是否等效。鉴于$ m $的几何理想三角剖分，我们还对四面体数的数量和二面角的下限进行了$ m $的收缩期长度的下限。
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.
