If the conjecture is true, a cube is topologically equivalent to a sphere No, the cube and sphere are homeomorphic regardless. (Pf: Points on S^3 are unit 4-v

If the conjecture is true, a cube is topologically equivalent to a sphere No, the cube and sphere are homeomorphic regardless. (Pf: Points on S^3 are unit 4-vectors. Projecting onto the unit cube is continuous and invertible) If the conjecture is true, and if you find yourself on a nice 3-surface, then you can conclude you're on the 3 sphere.