Jean-Philippe Furter

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 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.

Normal subgroup generated by a plane polynomial automorphism

We study the normal subgroup 〈f〉N generated by an element f ≠ id in the group G of complex plane polynomial automorphisms having Jacobian determinant 1. On the one hand, if f has length at most 8 relative to the classical amalgamated product structure of G, we prove that 〈f〉N = G. On the other hand, if f is a sufficiently generic element of even length at least 14, we prove that 〈f〉N ≠ G.

Extension of Automorphisms of Rational Smooth Affine Curves

We provide the existence, for every complex rational smooth affine curve

Locally finite polynomial endomorphisms

\Gamma

On the length of polynomial automorphisms of the affine plane

, of a linear action of

THE TAME AUTOMORPHISM GROUP OF AN AFFINE QUADRIC THREEFOLD ACTING ON A SQUARE COMPLEX

\mathrm{Aut}(\Gamma)

Plane polynomial automorphisms of fixed multidegree

on the affine 3-dimensional space

Some families of polynomial automorphisms

\mathbb{A}^3

On the degree of the inverse of an automorphism of the affine space

, together with a

A characterization of semisimple plane polynomial automorphisms

\mathrm{Aut}(\Gamma)