Two closed simply connected 4-manifolds are homeomorphic iff they have the same bilinear form and the same Kirby-Siebenmann invariant . Any can be realized by such a manifold. If is odd for some , then either value of can be realized also. However, if is always even, then is determined by , being congruent to 1/8 of the signature of . Here, is a symmetric bilinear form with determinant (Milnor).
In particular, if is a homotopy sphere, then and , so is homeomorphic to .