Coarse embeddings at infinity and generalized expanders at infinity
Operator Algebras
2022-07-18 v2 Group Theory
Metric Geometry
Abstract
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.
Cite
@article{arxiv.2206.11151,
title = {Coarse embeddings at infinity and generalized expanders at infinity},
author = {Jintao Deng and Liang Guo and Qin Wang and Yazhou Zhang},
journal= {arXiv preprint arXiv:2206.11151},
year = {2022}
}
Comments
20 pages