The open quadrant problem: A topological proof

In this work we present a new polynomial map $f:=(f_1,f_2):{\mathbb R}^2\to{\mathbb R}^2$whoseimageistheopenquadrant${x>0,y>0}\subset{\mathbb R}^2$. The proof of this fact involves arguments of topological nature that avoid hard computer calculations. In addition each polynomial $f_i\in \mathbb{R}[\mathtt{x},\mathtt{y}]$ has degree $\le 16$ and only $11$ monomials, becoming the simplest known map solving the open quadrant problem.