Eigenvalues of hyperbolic elements in Kleinian groups
Eigenvalues of hyperbolic elements in Kleinian groups
复制标题
克莱因群中双曲元素的特征值
DOI：
10.1090/conm/510/10026
复制
发表时间：
2010
影响因子：
4.9
通讯作者：
A. Reid
中科院分区：
文献类型：
--
作者：
D. Long;A. Reid
设Γ为无扭Kleinian群，使M = H/Γ为可定向双曲3流形。Γ的非平凡元素分为抛物线型和双曲型。如果γ∈Γ是双曲的，那么γ在H中有一个轴投射到M中的封闭测地线gγ（它只依赖于Γ中γ的共轭类）。元素γ通过平移和可能绕轴旋转作用于其轴。对于特征值，如果γ∈Γ是双曲的，我们令
Let Γ be a torsion-free Kleinian group, so that M = H/Γ is an orientable hyperbolic 3-manifold. The non-trivial elements of Γ are classified as either parabolic or hyperbolic. If γ ∈ Γ is hyperbolic, then γ has an axis in H which projects to a closed geodesic gγ in M (which depends only on the conjugacy class of γ in Γ). The element γ acts on its axis by translating and possibly rotating around the axis. In terms of eigenvalues, if γ ∈ Γ is hyperbolic, we let