https://diffgeom.subwiki.org/w/index.php?action=history&feed=atom&title=Donaldson%27s_theoremDonaldson's theorem - Revision history2026-11-04T07:32:18ZRevision history for this page on the wikiMediaWiki 1.41.2https://diffgeom.subwiki.org/w/index.php?title=Donaldson%27s_theorem&diff=406&oldid=prevVipul: 1 revision2008-05-18T19:38:50Z<p>1 revision</p>
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</td></tr></table>Vipulhttps://diffgeom.subwiki.org/w/index.php?title=Donaldson%27s_theorem&diff=405&oldid=prevVipul at 18:23, 23 June 20072007-06-23T18:23:49Z<p></p>
<p><b>New page</b></p><div>{{result on possible differential structures}}<br />
==Statement==<br />
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Any positive-definite [[intersection form]] of a [[simply connected space|simply connected]] [[differential manifold]] is equivalent to the identity matrix (viz, it can be diagonalized to the identity matrix).<br />
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==Relation with other results==<br />
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===Freedman's theorem===<br />
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{{further|[[Freedman's theorem]]}}<br />
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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.</div>Vipul