An introduction to the Ribe program

Assaf Naor

doi:10.1007/s11537-012-1222-7

An introduction to the Ribe program

Assaf Naor

Research output: Contribution to journal › Article › peer-review

71 Scopus citations

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 language	English (US)
Pages (from-to)	167-233
Number of pages	67
Journal	Japanese Journal of Mathematics
Volume	7
Issue number	2
DOIs	https://doi.org/10.1007/s11537-012-1222-7
State	Published - Nov 2012
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

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

Access to Document

10.1007/s11537-012-1222-7

Cite this

@article{57bb79d2438947e2a0d5404863fa5ca5,

title = "An introduction to the Ribe program",

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.",

keywords = "bi-Lipschitz and coarse invariants, local theory of Banach spaces, metric embeddings",

author = "Assaf Naor",

note = "Funding Information: Acknowledgements. I am grateful to Larry Guth and Manor Mendel for helpful suggestions. The research presented here is supported in part by NSF grant CCF-0832795, BSF grant 2010021, and the Packard Foundation.",

year = "2012",

month = nov,

doi = "10.1007/s11537-012-1222-7",

language = "English (US)",

volume = "7",

pages = "167--233",

journal = "Japanese Journal of Mathematics",

issn = "0289-2316",

publisher = "Springer",

number = "2",

}

TY - JOUR

T1 - An introduction to the Ribe program

AU - Naor, Assaf

N1 - Funding Information: Acknowledgements. I am grateful to Larry Guth and Manor Mendel for helpful suggestions. The research presented here is supported in part by NSF grant CCF-0832795, BSF grant 2010021, and the Packard Foundation.

PY - 2012/11

Y1 - 2012/11

N2 - 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.

AB - 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.

KW - bi-Lipschitz and coarse invariants

KW - local theory of Banach spaces

KW - metric embeddings

UR - https://www.scopus.com/pages/publications/84869210302

UR - https://www.scopus.com/pages/publications/84869210302#tab=citedBy

U2 - 10.1007/s11537-012-1222-7

DO - 10.1007/s11537-012-1222-7

M3 - Article

AN - SCOPUS:84869210302

SN - 0289-2316

VL - 7

SP - 167

EP - 233

JO - Japanese Journal of Mathematics

JF - Japanese Journal of Mathematics

IS - 2

ER -

An introduction to the Ribe program

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this