Characterising trees and hyperbolic spaces by their boundaries

被引：0

作者：

Davies, Isobel ^{[1
]}

机构：

[1] Otto von Guericke Univ, Univ Pl 2, D-39106 Magdeburg, Germany

来源：

JOURNAL OF GEOMETRY | 2024年 / 115卷 / 02期

关键词：

trees; hyperbolic spaces; cross ratio; proper CAT(-1) spaces; visual boundary;

D O I：

10.1007/s00022-024-00726-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We use the language of proper CAT(-1) spaces to study thick, locally compact trees, the real, complex and quaternionic hyperbolic spaces and the hyperbolic plane over the octonions. These are rank 1 Euclidean buildings, respectively rank 1 symmetric spaces of non-compact type. We give a uniform proof that these spaces may be reconstructed using the cross ratio on their visual boundary, bringing together the work of Tits and Bourdon.

引用

页数：17

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