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Coarse non-amenability and coarse embeddings

Publikationsart Peer-reviewed
Publikationsform Originalbeitrag (peer-reviewed)
Publikationsdatum 2012
Autor/in G. N. Arzhantseva E. Guentner and J. Spakula,
Projekt Groupes sofiques: algèbre, analyse et dynamique
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Originalbeitrag (peer-reviewed)

Zeitschrift Geometric and Functional Analysis
Volume (Issue) 22(1)
Seite(n) 22 - 36
Titel der Proceedings Geometric and Functional Analysis


The concept of coarse embedding was introduced by Gromov in 1993. It plays an important role in the study of large-scale geometry of groups and the Novikov higher signature conjecture. Guoliang Yu's property A is a weak amenability-type condition that is satis ed by many known metric spaces. It implies the existence of a coarse embedding into a Hilbert space. We construct the rst example of a metric space with bounded geometry which coarsely embeds into a Hilbert space, but does not have property A (in other words, the rst example of the true coarse expander).