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- Donaldson's_theorem abstract "In mathematics, Donaldson's theorem states that a definite intersection form of a simply connected 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. It was proved by Simon Donaldson. Michael Freedman had previously shown that any unimodular symmetric bilinear form is realized as the intersection form of some closed, oriented four-manifold. Combining this result with the Serre classification theorem and Donaldson's theorem, several interesting results can be seen:1) Any non-diagonalizable intersection form gives rise to a four-dimensional topological manifold with no differentiable structure (so cannot be smoothed).2) Two smooth simply-connected 4-manifolds are homeomorphic, if and only if, their intersection forms have the same rank, signature, and parity.".
- Donaldson's_theorem wikiPageExternalLink 1214437665.
- Donaldson's_theorem wikiPageID "2180754".
- Donaldson's_theorem wikiPageRevisionID "592122249".
- Donaldson's_theorem hasPhotoCollection Donaldson's_theorem.
- Donaldson's_theorem subject Category:Differential_topology.
- Donaldson's_theorem subject Category:Quadratic_forms.
- Donaldson's_theorem subject Category:Theorems_in_topology.
- Donaldson's_theorem type Abstraction100002137.
- Donaldson's_theorem type Communication100033020.
- Donaldson's_theorem type Form106290637.
- Donaldson's_theorem type LanguageUnit106284225.
- Donaldson's_theorem type Message106598915.
- Donaldson's_theorem type Part113809207.
- Donaldson's_theorem type Proposition106750804.
- Donaldson's_theorem type QuadraticForms.
- Donaldson's_theorem type Relation100031921.
- Donaldson's_theorem type Statement106722453.
- Donaldson's_theorem type Theorem106752293.
- Donaldson's_theorem type TheoremsInTopology.
- Donaldson's_theorem type Word106286395.
- Donaldson's_theorem comment "In mathematics, Donaldson's theorem states that a definite intersection form of a simply connected 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. It was proved by Simon Donaldson. Michael Freedman had previously shown that any unimodular symmetric bilinear form is realized as the intersection form of some closed, oriented four-manifold.".
- Donaldson's_theorem label "Donaldson's theorem".
- Donaldson's_theorem sameAs m.06sxvv.
- Donaldson's_theorem sameAs Q5295351.
- Donaldson's_theorem sameAs Q5295351.
- Donaldson's_theorem sameAs Donaldson's_theorem.
- Donaldson's_theorem wasDerivedFrom Donaldson's_theorem?oldid=592122249.
- Donaldson's_theorem isPrimaryTopicOf Donaldson's_theorem.