Difference between revisions of "Donaldson's theorem"
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Latest revision as of 19:38, 18 May 2008
Template:Result on possible differential structures
Statement
Any positivedefinite intersection form of a simply connected differential manifold is equivalent to the identity matrix (viz, it can be diagonalized to the identity matrix).
Relation with other results
Freedman's theorem
Further information: Freedman's theorem
Michael Freedman showed that every positive definite unimodular symmetric bilinear form of dimension 4 can be realized as the intersection form of a topological manifold of dimension 4. This, along with Donaldson's theorem, shows that there are topological manifolds with no differential structure.