Appendix A . The Cremona group is not an amalgam Yves

Let k be a field. The Cremona group Bir(Pk) of k in dimension d is defined as the group of birational transformations of the d-dimensional k-affine space. It can also be described as the group of k-automorphisms of the field of rational functions k(t1, . . . , td). We endow it with the discrete topology. Let us say that a group has Property (FR)∞ if it satisfies the following (1) For every isometric action on a complete real tree, every element has a fixed point.