I wonder if their is any technological implementation from solving poincare conjecture outside the mathematics. I am not a mathematician but I suspect their is.
No. The proof <i>itself</i> is totally useless, the technological consequences of it are nonexistent.<p>The interesting part are the tools developed to solve it and a better understanding about the geometrical properties of the euclidean space.<p>Mathematics is interesting and useful because it gives us tools for investigation abstract problems. The proof of one particular theorem is rarely more interesting then the mathematical foundations behind it.<p>Behind the Riemann hypothesis you will find a century of deep investigation into the structure of 3D space and its foundations, with incountably many applications. The proof of the theorem was a prestige object, demonstrating that the proover had a very deep grasp on the subject matter. But even in this case, the Ricci Flow is probably a far more interesting object from a technological perspective.