Geodesic
Topologies and structures of the Cremona groups
Jérémy Blanc1 ; Jean-Philippe Furter2
1 Universität Basel, Basel, Switzerland
2 University of La Rochelle, La Rochelle, France
Annals of mathematics, Tome 178 (2013) no. 3, pp. 1173-1198.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We study the algebraic structure of the $n$-dimensional Cremona group and show that it is not an algebraic group of infinite dimension (ind-group) if $n\ge 2$. We describe the obstruction to this, which is of a topological nature. By contrast, we show the existence of a Euclidean topology on the Cremona group which extends that of its classical subgroups and makes it a topological group.
DOI : 10.4007/annals.2013.178.3.8

Jérémy Blanc 1 ; Jean-Philippe Furter 2

1 Universität Basel, Basel, Switzerland
2 University of La Rochelle, La Rochelle, France 
@article{10_4007_annals_2013_178_3_8,
     author = {J\'er\'emy Blanc and Jean-Philippe Furter},
     title = {Topologies and structures of the {Cremona} groups},
     journal = {Annals of mathematics},
     pages = {1173--1198},
     publisher = {mathdoc},
     volume = {178},
     number = {3},
     year = {2013},
     doi = {10.4007/annals.2013.178.3.8},
     mrnumber = {3092478},
     zbl = {06220731},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2013.178.3.8/}
}
TY  - JOUR
AU  - Jérémy Blanc
AU  - Jean-Philippe Furter
TI  - Topologies and structures of the Cremona groups
JO  - Annals of mathematics
PY  - 2013
SP  - 1173
EP  - 1198
VL  - 178
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4007/annals.2013.178.3.8/
DO  - 10.4007/annals.2013.178.3.8
LA  - en
ID  - 10_4007_annals_2013_178_3_8
ER  - 
%0 Journal Article
%A Jérémy Blanc
%A Jean-Philippe Furter
%T Topologies and structures of the Cremona groups
%J Annals of mathematics
%D 2013
%P 1173-1198
%V 178
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4007/annals.2013.178.3.8/
%R 10.4007/annals.2013.178.3.8
%G en
%F 10_4007_annals_2013_178_3_8
Jérémy Blanc; Jean-Philippe Furter. Topologies and structures of the Cremona groups. Annals of mathematics, Tome 178 (2013) no. 3, pp. 1173-1198. doi : 10.4007/annals.2013.178.3.8. http://geodesic.mathdoc.fr/articles/10.4007/annals.2013.178.3.8/

Cité par Sources :