Topologies and structures of the Cremona groups
Algebraic Geometry
2013-08-26 v3 General Topology
Group Theory
Abstract
We study the algebraic structure of the -dimensional Cremona group and show that it is not an algebraic group of infinite dimension (ind-group) if . 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.
Cite
@article{arxiv.1210.6960,
title = {Topologies and structures of the Cremona groups},
author = {Jérémy Blanc and Jean-Philippe Furter},
journal= {arXiv preprint arXiv:1210.6960},
year = {2013}
}
Comments
20 pages, to appear in Annals of Mathematics