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Freedman's theorem

Definition

Every positive-definite unimodular symmetric bilinear form can be realized as the intersection form of a topological manifold if its dimension is less than or equal to 4.

Relation with other results

Donaldson's theorem

Further information: Donaldson's theorem

Donaldson's theorem states that the intersection form arising from any differential manifold of dimension 4 must be diagonalizable to the identity matrix. This, along with Freedman's theorem, demonstrates that there are topological 4-manifolds that do not admit any differential structure.