Two-generator free Kleinian groups and hyperbolic displacements
Two-generator free Kleinian groups and hyperbolic displacements
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DOI：
10.2140/agt.2014.14.3141
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发表时间：
2009-11
影响因子：
0.7
通讯作者：
.Ilker S. Yuce-Ilker-S.-Yuce-102800584
中科院分区：
文献类型：
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作者：
.Ilker S. Yuce-Ilker-S.-Yuce-102800584
由Culler和Shalen证明的log 3定理指出，双曲3空间H3中的每一点都被H3的一个非对易等距移动至少log 3的距离，条件是生成一个无挠的离散群，该群不是余紧的，并且不包含抛物。这个定理是许多技术的基础，这些技术为可定向的闭双曲3-流形的体积提供了较低的估计，这些流形的基本群没有有限指数的2-生成子群，因此，可以深入了解这些流形的拓扑性质。在log 3定理的假设下，本文的主要结果表明，H3中的每一点都被其中一个移动了至少logp 5C 3 p2的距离，
The log3 theorem, proved by Culler and Shalen, states that every point in the hyperbolic 3‐space H 3 is moved a distance at least log3 by one of the noncommuting isometries or of H 3 provided that and generate a torsion-free, discrete group which is not cocompact and contains no parabolic. This theorem lies in the foundations of many techniques that provide lower estimates for the volumes of orientable, closed hyperbolic 3‐manifolds whose fundamental groups have no 2‐ generator subgroup of finite index and, as a consequence, gives insights into the topological properties of these manifolds. Under the hypotheses of the log3 theorem, the main result of this paper shows that every point in H 3 is moved a distance at least log p 5C3 p 2 by one of the