课程名称：Donaldson Question: “Tamed to Compatible"
课程概况：In these talks,we show that on any tamed closed almost complex four-manifold (M,J) whosedimension of J-anti-invariant cohomology is equal to self-dual second Bettinumber minus one, there exists a new symplectic form compatible with the givenalmost complex structure J. In particular, if the self-dual second Betti numberis one, we give an affirmative answer to Donaldson question for tamed closedalmost complex four-manifolds that is a conjecture in joint paper of Tosatti,Weinkove and Yau.
Our approach isalong the lines used by Buchdahl to give a unified proof of the Kodairaconjecture. Thus, our main result gives an affirmative answer to the Kodairaconjecture in symplectic version.