Topologies and structures of the Cremona groups
By J. Blanc, Jean–Philippe Furter. 2012
82 citations recorded by the source corpus.
We study the algebraic structure of the n-dimensional Cremona group and show that it is not an algebraic group of innite dimension (ind-group) if n 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.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/717c28d182d15e18cc98c300da83fdece6674c75
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In Algebra and Number Theory
In Geometry and Topology
In Statistical and Nonlinear Physics
Citations in the corpus
- Dynamical degrees of birational transformations of projective surfaces (2013, background): “The set Bird(P(2)k) of all birational transformations of degree d is naturally endowed with the structure of an algebraic variety (see [10]); we denote by F the Zariski closure of the set { fi}i≥0 in Bird(P(2)k).”