Metric Dichotomies

Details Metric Dichotomies Metric Dichotomies

2007-10-10

arxiv.org/abs/0710.1994v3

in Goulnara Arzhantseva, Alain Valette (eds.) Limits of graphs in group theory and computer science, EPFL Press, 2009

Mathematics

Metric Geometry

Lecture notes. 14 pages, 5 figures. Final version with only minor changes from the previous version

Scientific paper

These are notes from talks given at ICMS, Edinburgh, 4/2007 ("Geometry and Algorithms workshop") and at Bernoulli Center, Lausanne 5/2007 ("Limits of graphs in group theory and computer science"). We survey the following type of dichotomies exhibited by certain classes X of finite metric spaces: For every host space H, either all metrics in X embed almost isometrically in H, or the distortion of embedding some metrics of X in H is unbounded.

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