Leírás
Előadó: Thiebout Delabie
Cím: Box spaces of the free group.
Absztrakt: In the study of metric spaces, box spaces can provide useful examples of metric spaces with exceptional large scale properties. Two of these properties are coarse embeddability into a Hilbert space and containing an expander. These two properties are mutually exclusive. A box space is created using a group and a sequence of normal subgroups. Box spaces created from amenable group embed into a Hilbert space, while those created from a group with property (T) are expanders. As for groups which are neither amenable, nor have property (T) it is not clear which property the box spaces have. For the free group there exists box spaces that embed into a Hilbert space and there exists box spaces that are expanders. We will construct a box space of the free group with neither property.