The Donaldson tamed-to-compatible conjecture asserts that an almost complex structure 
on a closed connected four-dimensional smooth
manifold that is tamed by some symplectic form
admits a compatible symplectic form. The almost
complex structure is fixed, while the form may change. The assertion does not
prescribe the cohomology class of every given
taming form.
Donaldson Tamed-to-Compatible Conjecture
See also
Almost Complex Structure, Cohomology Class, Intersection Form, Symplectic TamingExplore with Wolfram|Alpha
References
Donaldson, S. K. "Two-Forms on Four-Manifolds and Elliptic Equations." In Inspired by S. S. Chern: A Memorial Volume in Honor of a Great Mathematician (Ed. P. A. Griffiths). Hackensack, NJ: World Scientific, pp. 153-172, 2006. https://doi.org/10.1142/9789812772688_0007.Cite this as:
Weisstein, Eric W. "Donaldson Tamed-to-Compatible Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DonaldsonTamed-to-CompatibleConjecture.html