About: Donaldson's theorem

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

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rdfs:label	Donaldson's theorem (en) ドナルドソンの定理 (ja)
rdfs:comment	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. (en) 数学では、ドナルドソンの定理(Donaldson's theorem)は、次元 4 の単連結な滑らかな多様体(smooth manifold)の定値(definite)な交叉形式は、対角化可能であるという定理である。交叉形式が正定値（負定値）であれば、交叉形式は整数上の単位行列（負の単位行列）に対角化可能である。 (ja)
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dcterms:subject	Quadratic forms Theorems in topology Differential topology
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Link from a Wikipage to another Wikipage	Homeomorphic Betti number Definite quadratic form Donaldson theory Signature of a quadratic form Quadratic forms Compact space Cone (linear algebra) Theorems in topology Mathematics Gauge theory (mathematics) Clifford Taubes Simon Donaldson dbr:Complex_projective_plane Identity matrix Parity (mathematics) American Mathematical Society Differential topology Fields medal Differential topology Journal of Differential Geometry Rank (linear algebra) Atiyah–Singer index theorem Intersection form (4-manifold) Karen Uhlenbeck Cobordism Moduli space Diagonalizable matrix Dimension Michael Freedman Orientability Yang–Mills equations Topological manifold Smooth manifold Unimodular lattice Principal bundle Rokhlin's theorem Simply connected Four-manifold Unimodular symmetric bilinear form Differentiable structure dbr:Serre_classification_theorem
sameAs	Donaldson's theorem Donaldson's theorem Donaldson's theorem Donaldson's theorem Donaldson's theorem
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has abstract	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. (en) 数学では、ドナルドソンの定理(Donaldson's theorem)は、次元 4 の単連結な滑らかな多様体(smooth manifold)の定値(definite)な交叉形式は、対角化可能であるという定理である。交叉形式が正定値（負定値）であれば、交叉形式は整数上の単位行列（負の単位行列）に対角化可能である。 (ja)
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foaf:isPrimaryTopicOf	wikipedia-en:Donaldson's_theorem
is Link from a Wikipage to another Wikipage of	List of mathematical jargon Donaldson theory E8 manifold Intersection form of a 4-manifold Gauge theory (mathematics) Clifford Taubes Simon Donaldson 4-manifold Differential structure Differential topology Differentiable manifold Donaldson theorem Casson handle Yang–Mills equations Unimodular lattice List of theorems
is Wikipage redirect of	Donaldson theorem
is foaf:primaryTopic of	wikipedia-en:Donaldson's_theorem

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