SEPARATION OF RELATIVELY QUASICONVEX SUBGROUPS
SEPARATION OF RELATIVELY QUASICONVEX SUBGROUPS
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相对拟凸子群的分离
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
Eduardo Martínez
中科院分区：
文献类型：
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作者：
J. Manning;Eduardo Martínez
我们证明了，如果所有双曲群是剩余有限的，这些声明如下：在相对双曲群的周边结构组成的n-生成幂零子群，相对拟凸子群是可分的;几何有限子群的非一致格在秩一对称空间是可分的;克莱因群是子群可分的。我们还证明了有限体积双曲3-流形的LERF将遵循闭双曲3-流形的LERF。我们证明了这些事实减少，通过组合和填充定理，一个相对双曲群G的一个相对拟凸子群的可分离性的双曲商NG的拟凸子群。然后应用Agol、格罗夫斯和Manning的结果。
We show that if all hyperbolic groups are residually finite, these statements follow: In relatively hyperbolic groups with peripheral structures consisting of finitely generated nilpotent subgroups, relatively quasiconvex subgroups are separable; geometrically finite subgroups of nonuniform lattices in rank one symmetric spaces are separable; Kleinian groups are subgroup separable. We also show that LERF for finite volume hyperbolic 3-manifolds would follow from LERF for closed hyperbolic 3-manifolds. We prove these facts by reducing, via combination and filling theorems, the separability of a relatively quasiconvex subgroup of a relatively hyperbolic group G to that of a quasiconvex subgroup of a hyperbolic quotient N G. A result of Agol, Groves, and Manning is then applied.