Abstract of Urs Lang’s course

Injective metric spaces, or absolute 1-Lipschitz retracts,
share a number of properties with CAT(0) spaces. In the
1960es, Isbell showed that every metric space possesses an
essentially unique injective hull (envelope), and Cohen
established the corresponding result in the linear category.
Twenty years later, Isbell’s construction was rediscovered
and named tight span by Dress. Injective hulls have received
attention in Banach space theory, discrete optimization,
metric fixed point theory, and even in phylogenetic analysis,
but have not yet been much explored in the context of metric
geometry and geometric group theory. The first lecture will
survey some recent results in this area, in particular on
injective hulls of Gromov hyperbolic spaces and groups. The
subsequent lectures will provide a detailed discussion of
these and further results on the structure of injective hulls
of discrete metric spaces, together with the necessary
background.

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About metric2011

metric2011 is a program of Centre Emile Borel, an activity of Institut Henri Poincaré, 11 rue Pierre et Marie Curie, 75005 Paris, France. See http://www.math.ens.fr/metric2011/
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