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.

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Authors

Jérémy Blanc

Universität Basel, Basel, Switzerland

Jean-Philippe Furter

University of La Rochelle, La Rochelle, France