Donaldson’s theorem

Theorem Let M be a smooth simply connected, closed 4- manifoldMathworldPlanetmath. If the bilinear formMathworldPlanetmathPlanetmath induced on H2(M;𝒁) by the cup productMathworldPlanetmath is positive definitePlanetmathPlanetmath, then it may be represented by the identity matrixMathworldPlanetmath.

One application is the existence of exotic 𝑹4’s. See Donaldson Freedman exotic R4.

Title Donaldson’s theorem
Canonical name DonaldsonsTheorem
Date of creation 2013-03-22 15:37:30
Last modified on 2013-03-22 15:37:30
Owner whm22 (2009)
Last modified by whm22 (2009)
Numerical id 9
Author whm22 (2009)
Entry type Theorem
Classification msc 57R12
Classification msc 14J80
Related topic exoticR4s
Related topic DonaldsonFreedmanexoticR4
Related topic DonaldsonFreedmanExoticR4
Related topic ExoticR4s