On the elementary theory of free groups

Frédéric Paulin

Séminaire Bourbaki (2002-2003)

  • Volume: 45, page 363-402
  • ISSN: 0303-1179

Abstract

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Sela has announced a complete solution of Tarski’s problem, who asked around 1945 what are the finitely generated groups having the same elementary theory as a free group. We will talk about the works of Remeslennikov, Kharlampovich-Myasnikov, Sela, Champetier-Guirardel and others on the structure of the limit groups (the finitely generated groups thar are “limits”of free groups, or equivalently that have the same universal theory as a free group. We will indicate some of the tools used by Sela (including technics of Rips, Rips-Sela, Bestvina-Feighn and others on group actions on trees).

How to cite

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Paulin, Frédéric. "Sur la théorie élémentaire des groupes libres." Séminaire Bourbaki 45 (2002-2003): 363-402. <http://eudml.org/doc/252138>.

@article{Paulin2002-2003,
abstract = {Sela a annoncé une solution complète d’un problème de Tarski, qui demanda vers 1945 quels sont les groupes de type fini qui ont la même théorie élémentaire qu’un groupe libre. Nous discuterons des travaux de Remeslennikov, Kharlampovich-Myasnikov, Sela, Champetier-Guirardel et autres sur la structure des groupes limites (les groupes de type fini qui sont “limites”de groupes libres, ou encore, qui ont la même théorie universelle qu’un groupe libre). Nous indiquerons quelques outils utilisés par Sela (dont des techniques de Rips, Rips-Sela, Bestvina-Feighn et autres sur les actions de groupes sur les arbres).},
author = {Paulin, Frédéric},
journal = {Séminaire Bourbaki},
keywords = {first order formula; elementary theory; Tarski’s problem; free group; limit group; groups action on trees},
language = {fre},
pages = {363-402},
publisher = {Association des amis de Nicolas Bourbaki, Société mathématique de France},
title = {Sur la théorie élémentaire des groupes libres},
url = {http://eudml.org/doc/252138},
volume = {45},
year = {2002-2003},
}

TY - JOUR
AU - Paulin, Frédéric
TI - Sur la théorie élémentaire des groupes libres
JO - Séminaire Bourbaki
PY - 2002-2003
PB - Association des amis de Nicolas Bourbaki, Société mathématique de France
VL - 45
SP - 363
EP - 402
AB - Sela a annoncé une solution complète d’un problème de Tarski, qui demanda vers 1945 quels sont les groupes de type fini qui ont la même théorie élémentaire qu’un groupe libre. Nous discuterons des travaux de Remeslennikov, Kharlampovich-Myasnikov, Sela, Champetier-Guirardel et autres sur la structure des groupes limites (les groupes de type fini qui sont “limites”de groupes libres, ou encore, qui ont la même théorie universelle qu’un groupe libre). Nous indiquerons quelques outils utilisés par Sela (dont des techniques de Rips, Rips-Sela, Bestvina-Feighn et autres sur les actions de groupes sur les arbres).
LA - fre
KW - first order formula; elementary theory; Tarski’s problem; free group; limit group; groups action on trees
UR - http://eudml.org/doc/252138
ER -

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