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Dynamics, Geometry and Groups Seminar

Speaker: Abdul Zalloum (³ÉÈË´óƬ)

Title: Injective metric spaces

Abstract:
A metric space is said to be injective if it is an injective object in the category of metric spaces with respect to 1-Lipshitz maps. In other words, X is injective if for any 1-Lipshitz map f: Y→X and any isometric embedding i: Y→Z, there is a 1-Lipshitz map f':Z -->X with f'i= f. I’ll start my talk with the above definition, then, from the definition alone, I’ll derive a series of striking properties of injective metric spaces—so strong that, at first glance, they make such spaces seem almost too good to exist. I will then show you that they are all over the place: every metric space admits an equivariant isometric embedding into an injective space.