Appendix A. The Cremona group is not an amalgam Yves de Cornulier Let k be a field. The Cremona group Bir(P

For example, the following result was proved: a cyclic group of prime order is conjugate to a linear automorphism of the plane if and only if it does not fix a curve of positive

The last step is based on the classification of al- gebraic groups of transformations of surfaces, and the fact that every subgroup of SL 2 (k) with Kazhdan property (T) is finite;

Remark 2 The same arguments show that a Zariski dense representation of a K¨ ahler group Γ in a noncompact simple Lie group G (with trivial center and not isomorphic to PSL 2 ( R

The length in Aut( A 2 ) is then easy to compute, by writing an element in a reduced form (i.e. as a product of elements of Aff 2 and Jonq p, A 2 where two consecutive elements do

Repeat the exer- cise in homology, for cor G×K H×K and tr G×K H×K (in homology, the hypothesis that G be finite can be supressed, but of course we need [G : H ] < ∞ for the

The bouquet bch(E , A ) will be called the bouquet of Chern characters of the bundle E with connection A (in fact, we will have to modify the notion of G-equivariant vector bundle

Let us denote by RG perm p the category of all p {permutation RG {modules. The following proposition generalizes to p {permutation modules a result which is well known for

One can consult [43] for a simpler proof of Lemma 2.16 and Theorem 2.10 in the case of a group acting on a tree, and for small cancellation theory in the context of Aut[k 2 ] and