 This Arf invariant is obviously 0 if formula_29 is a sphere, so the Kervaire–Milnor theorem is a special case.A generalization of the Freedman-Kirby theorem to topological (rather than smooth) manifolds states that
where formula_40 is the Kirby–Siebenmann invariant of "M".The Kirby–Siebenmann invariant of "M" is 0 if "M" is smooth.