Coarse non-amenability and coarse embeddings
Seminar Room 1, Newton Institute
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 satisfied by many known metric spaces. It implies the existence of a coarse embedding into a Hilbert space.
We construct the first example of a metric space with bounded geometry which coarsely embeds into a Hilbert space, but does not have property A. This is a joint work with Erik Guentner and Jan Spakula.