论文标题
无穷大的粗嵌入和无穷大的广义扩展器
Coarse embeddings at infinity and generalized expanders at infinity
论文作者
论文摘要
我们将无穷大嵌入的粗嵌入概念引入了希尔伯特空间中的公制空间中，这是纤维粗嵌入的概念的削弱，并且对格罗莫夫的粗嵌入概念的概括很广泛。事实证明，一个残留有限的群体在且仅当一个（或等效地，每个）盒子空间中，将粗糙的嵌入到希尔伯特空间中，该盒子空间承认无穷大的粗糙嵌入到希尔伯特空间中。此外，我们介绍了无穷大的广义扩展器的概念，并表明它是对无穷大的粗嵌入性的阻碍。
We introduce a notion of coarse embedding at infinity into Hilbert space for metric spaces, which is a weakening of the notion of fibred coarse embedding and a far generalization of Gromov's concept of coarse embedding. It turns out that a residually finite group admits a coarse embedding into Hilbert space if and only if one (or equivalently, every) box space of the group admits a coarse embedding at infinity into Hilbert space. Moreover, we introduce a concept of generalized expander at infinity and show that it is an obstruction to coarse embeddability at infinity.
