PSL(2, C), the exponential and some new free groups

Daniel Panazzolo (1)

1 Université de Haute-Alsace (UHA) - Université de Haute-Alsace (UHA) Mulhouse - Colmar

We prove a normal form result for the groupoid of germs generated by PSL(2, C) and the exponential map. We discuss three consequences of this result: (1) a generalization of a result of Cohen about the group of translations and powers, which gives a positive answer to a problem posed by Higman; (2) a proof that the subgroup of Homeo(R, +∞) generated by the positive affine maps and the exponential map is iso-morphic to a HNN-extension; (3) a finitary version of the immiscibility conjecture of Ecalle-Martinet-Moussu-Ramis

Domaines: Géométrie algébrique [math.AG]; Systèmes dynamiques [math.DS]

Daniel Panazzolo. PSL(2, C), the exponential and some new free groups. Quarterly Journal of Mathematics, 2018, 69 (1), pp.75-117. ⟨10.1093/qmath/hax032⟩. ⟨hal-02907175⟩