Donaldson’s theorem

Theorem Let $M$ be a smooth simply connected, closed 4- manifold. If the bilinear form induced on $H_2(M;𝒁)$ by the cup product is positive definite, then it may be represented by the identity matrix.

One application is the existence of exotic ${𝑹}^4$’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