Theorems in topology | Quadratic forms | Differential topology

Donaldson's theorem

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 of the theorem required the manifold to be simply connected, but it was later improved to apply to 4-manifolds with any fundamental group. (Wikipedia).

Donaldson's theorem
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Related pages

Topological manifold | Principal bundle | Diagonalizable matrix | Unimodular lattice | Donaldson theory | Complex projective plane | Gauge theory (mathematics) | Betti number | Atiyah–Singer index theorem | Identity matrix | Definite quadratic form | Yang–Mills equations | Dimension | Rokhlin's theorem | Mathematics | Orientability | Cobordism | Differential topology | Compact space | Parity (mathematics) | Moduli space | Rank (linear algebra)