论文标题
算术双曲2和3个manifolds的收缩
Systoles of Arithmetic Hyperbolic 2- and 3-Manifolds
论文作者
论文摘要
在本文中，我们研究了算术双曲2和3个manifolds的收缩。我们的第一个结果是构建无限的许多算术双曲2和3个manifolds，它们是成对不可固定的，所有这些都具有相同的收缩期，并且其体积明确界定。我们的第二个结果固定了正数X，并给出了最小体积的算术双曲2或3个manifold的上限，该算术双曲线2或3个manifold大于x。我们通过确定x的某些较小值的结论，在q（i）上，Q或3个manifold上的主算术双曲的2个manifold的体积最小，其收缩期大于x的q（i）。
In this paper we study the systoles of arithmetic hyperbolic 2- and 3-manifolds. Our first result is the construction of infinitely many arithmetic hyperbolic 2- and 3-manifolds which are pairwise noncommensurable, all have the same systole, and whose volumes are explicitly bounded. Our second result fixes a positive number x and gives an upper bound for the least volume of an arithmetic hyperbolic 2- or 3-manifold whose systole is greater than x. We conclude by determining, for certain small values of x, the least volume of a principal arithmetic hyperbolic 2-manifold over Q or 3-manifold over Q(i) whose systole is greater than x.
