Two-dimensional simply connected abelian locally Nash groups

Abstract

The aim of this paper is to give a description of simply connected abelian locally Nash groups of dimension $2$. Along the way we prove that, for any $n\ge 2$, a locally Nash structure over $({\mathbb{R}}^n,+)$ can be characterized via a meromorphic map admitting an algebraic addition theorem.

The results of this paper have been polished and extended. They appear in arXiv:1704.08514, arXiv:1707.08171 and arXiv:1711.00806