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Is the Cremona group compactly presented?

Le : 21/11/2014 14h00
Par : Susanna Zimmermann (Bâle)
Lieu : I 001
Lien web :
Résumé : We consider the group of birational transformations of the complex n-dimensional projective space, the Cremona group Cr(n). Any algebraic subgroup carries two topologies, the Euclidean topology and the Zariski topology. There exists a topology on Cr(n) which restricted to any algebraic subgroup is the Euclidean topology, and which moreover makes Cr(n) a Hausdorff topological group. I will recall the notion of compact presentation of topological Hausdorff groups and discuss why the Cremona group of the complex plane is compactly presented and then discuss the question whether the subgroup of transformations defined over the real numbers is compactly presented as well.