An introduction to the Ribe program

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Abstract

We survey problems, results, ideas, and recent progress in the Ribe program. The goal of this research program, which is motivated by a classical rigidity theorem of Martin Ribe, is to obtain structural results for metric spaces that are inspired by the local theory of Banach spaces. We also present examples of applications of the Ribe program to several areas, including group theory, theoretical computer science, and probability theory.

Original languageEnglish (US)
Pages (from-to)167-233
Number of pages67
JournalJapanese Journal of Mathematics
Volume7
Issue number2
DOIs
StatePublished - Nov 21 2012
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • bi-Lipschitz and coarse invariants
  • local theory of Banach spaces
  • metric embeddings

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