Relations between Various Boundaries of Relatively hyperbolic Groups
Relations between Various Boundaries of Relatively hyperbolic Groups
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相对双曲群的各种边界之间的关系
DOI：
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发表时间：
2012
影响因子：
0.8
通讯作者：
H. Tran
中科院分区：
文献类型：
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作者：
H. Tran
Suppose a group G is relatively hyperbolic with respect to a collection ℙ of its subgroups and also acts properly, cocompactly on a CAT(0) (or δ-hyperbolic) space X. The relatively hyperbolic structure provides a relative boundary ∂(G, ℙ). CAT(0) 结构在无穷大 ∂X 处提供了不同的边界。在本文中，我们研究了这两个无穷远空间之间的联系。 In particular, we show that ∂(G, ℙ) is G-equivariantly homeomorphic to the space obtained from ∂X by identifying the peripheral limit points of the same type.
Suppose a group G is relatively hyperbolic with respect to a collection ℙ of its subgroups and also acts properly, cocompactly on a CAT(0) (or δ-hyperbolic) space X. The relatively hyperbolic structure provides a relative boundary ∂(G, ℙ). The CAT(0) structure provides a different boundary at infinity ∂X. In this paper, we examine the connection between these two spaces at infinity. In particular, we show that ∂(G, ℙ) is G-equivariantly homeomorphic to the space obtained from ∂X by identifying the peripheral limit points of the same type.