Waldhausen conjectured what is now the Jaco–Shalen–Johannson-decomposition of 3-manifolds, which is a decomposition of 3-manifolds along spheres and incompressible tori.
The mathematician Waldhausen initially suggested a technique that is now referred to as the Jaco–Shalen–Johannson-decomposition of 3-manifolds. This method entails dividing these three-dimensional spaces into parts based on spheres and non-contractible tori.