The metric compactification

Marc Rieffel

2.10pm-4.00 pm March 8

939 Evans Hall, Berkeley
ABSTRACT: From my investigation of group algebras (for non-commutative discrete groups) as compact quantum metric spaces (often in connection with a word-length function from a finite generating subset), I was led to the definition of a compactification for any locally compact metric space. It turned out that this compactification is equivalent to a compactification introduced by Gromov, but little-studied, in contrast to Gromov's famous compactification for hyperbolic spaces. There is a strong relationship with geodesic rays. Already for Z with word-length distance from the generating set {3, 8, -3, -3}, for example, the picture is entertaining. There are many open questions.
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