CaltechAUTHORS
  A Caltech Library Service

Linear algebraic groups and countable Borel equivalence relations

Adams, Scot and Kechris, Alexander S. (2000) Linear algebraic groups and countable Borel equivalence relations. Journal of the American Mathematical Society, 13 (4). pp. 909-943. ISSN 0894-0347. https://resolver.caltech.edu/CaltechAUTHORS:20130524-130949007

[img]
Preview
PDF - Published Version
See Usage Policy.

393Kb

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20130524-130949007

Abstract

This paper is a contribution to the study of Borel equivalence relations on standard Borel spaces (i.e., Polish spaces equipped with their Borel structure). In mathematics one often deals with problems of classification of objects up to some notion of equivalence by invariants. Frequently these objects can be viewed as elements of a standard Borel space X and the equivalence turns out to be a Borel equivalence relation E on X. A complete classification of X up to E consists of finding a set of invariants I and a map c : X → I such that xEy ⇔ c(x) = c(y). For this to be of any interest both I and c must be explicit or definable and as simple and concrete as possible. The theory of Borel equivalence relations studies the set-theoretic nature of possible invariants and develops a mathematical framework for measuring the complexity of such classification problems.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1090/S0894-0347-00-00341-6DOIArticle
http://www.ams.org/journals/jams/2000-13-04/S0894-0347-00-00341-6/home.htmlPublisherArticle
Additional Information:© 2000 American Mathematical Society. Received by the editors March 27, 1999 and, in revised form, April 21, 2000. Article electronically published on June 23, 2000. The first author's research was partially supported by NSF Grant DMS 9703480. The second author's research was partially supported by NSF Grant DMS 9619880 and a Visiting Miller Research Professorship at U.C. Berkeley.
Funders:
Funding AgencyGrant Number
NSFDMS-9703480
NSFDMS-9619880
U. C. Berkeley Visiting Miller Research ProfessorshipUNSPECIFIED
Other Numbering System:
Other Numbering System NameOther Numbering System ID
MathSciNet ReviewMR1775739
Issue or Number:4
Classification Code:2000 MSC: Primary 03E15; Secondary 37A20
Record Number:CaltechAUTHORS:20130524-130949007
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20130524-130949007
Official Citation:Adams, Scott and Kechris, Alexander S. (2000) Linear algebraic groups and countable Borel equivalence relations. Journal of the American Mathematical Society, 13 (4). pp. 909-943.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38668
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:29 May 2013 22:37
Last Modified:03 Oct 2019 04:59

Repository Staff Only: item control page