Topologies and structures of the Cremona groups
  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. 
J\'er\'emy Blanc, Jean-Philippe Furter
math.AG math.GN math.GR