Filling invariants at infinity and the Euclidean rank of Hadamard spaces
Filling invariants at infinity and the Euclidean rank of Hadamard spaces
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填充无穷大不变量和哈达玛空间的欧几里得等级
DOI：
10.1155/imrn/2006/83090
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发表时间：
2005
影响因子：
1
通讯作者：
S. Wenger
中科院分区：
文献类型：
--
作者：
S. Wenger
本文研究了Brady和Farb在[BrFa]中定义的渐近填充不变量divk的一个同调版本，证明了它是所有适当紧致Hadamard空间即适当紧致CAT(0)-空间的拟等距不变量，并进一步证明了它可用于检测此类空间的欧氏秩。从而将[BrFa， Leu， Hin]的结果从非紧型对称空间的集合推广到Hadamard空间的集合。最后，我们证明了欧氏秩不大于k的非紧型对称空间和κ < 0的CAT(κ)-空间的第k次同调散度的最优增长。
In this paper we study a homological version of the asymptotic filling invariant divk defined by Brady and Farb in [BrFa] and show that it is a quasi-isometry invariant for all proper cocompact Hadamard spaces, i.e. proper cocompact CAT(0)-spaces, and that it can furthermore be used to detect the Euclidean rank of such spaces. We thereby extend results of [BrFa, Leu, Hin] from the setting of symmetric spaces of non-compact type to that of Hadamard spaces. Finally, we exhibit the optimal growth of the k-th homological divergence for symmetric spaces of non-compact type with Euclidean rank no larger than k and for CAT(κ)-spaces with κ < 0.