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    Space of symplectic forms

    Tian-Jun Li and Ai-Ko Liu
    ( Click here for pdf version )

    Let $M$ be a closed oriented smooth $4-$manifold admitting symplectic structures. We study the number of of equivalence classes of symplectic canonical classes on $M$. If $M$ has $b^+=1$, we prove there is a unique equivalence class. This result, together with results of Taubes and Witten, implies that the this number is finite for any $M$. We also study which second cohomology class on $M$ is represented by symplectic forms. In particular, if $M$ is minimal and has $b^+=1$, we show that every class of positive square has symplectic representatives.