The congruent number problem and the Birch-Swinnerton-Dyer conjecture

Abstract

By introducing a new point of view in Algebraic Topology relating elliptic curves in ${\mathbb{R}}^2$ and suitable bordism groups, the congruent number problem is solved showing that the Tunnell's theorem is also sufficient. This could be considered also an indirect proof that the Birch Swinnerton-Dyer conjecture is true.

35 pages, 4 figures