Donaldson's theorem
On when a definite intersection form of a smooth 4-manifold is diagonalisable / From Wikipedia, the free encyclopedia
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In mathematics, and especially differential topology and gauge theory, Donaldson's theorem states that a definite intersection form of a compact, oriented, smooth manifold of dimension 4 is diagonalisable. If the intersection form is positive (negative) definite, it can be diagonalized to the identity matrix (negative identity matrix) over the integers. The original version[1] of the theorem required the manifold to be simply connected, but it was later improved to apply to 4-manifolds with any fundamental group.[2]