Topologies and structures of the Cremona groups
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2012
- DOI:
- 10.48550/arXiv.1210.6960
- arXiv:
- arXiv:1210.6960
- Bibcode:
- 2012arXiv1210.6960B
- Keywords:
-
- Mathematics - Algebraic Geometry;
- Mathematics - General Topology;
- Mathematics - Group Theory;
- 14E07;
- 20G15;
- 54H11
- E-Print:
- 20 pages, to appear in Annals of Mathematics