%0 Journal Article
%T The solvable length of groups of local diffeomorphisms
%A Javier Rib¨Žn
%J Mathematics
%D 2014
%I arXiv
%X We are interested in the algebraic properties of groups of local biholomorphisms and their consequences. A natural question is whether the complexity of solvable groups is bounded by the dimension of the ambient space. In this spirit we show that $2n+1$ is the sharpest upper bound for the derived length of solvable subgroups of the group $\mathrm{Diff}({\mathbb C}^{n},0)$ of local complex analytic diffeomorphisms for $n=2,3,4,5$.
%U http://arxiv.org/abs/1406.0902v2