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Coarse non-amenability and coarse embeddings

Presented by: 
G Arzhantseva [Vienna]
Date: 
Wednesday 12th January 2011 - 14:00 to 15:00
Venue: 
INI Seminar Room 1
Abstract: 
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.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons