Infinite generation of some higher homotopy groups of symplectomorphism groups is proved for n-point Kahler blowups of tori, K3 surfaces, and Enriques surfaces with non-resonant Kahler classes.
Family Seiberg-Witten invariants and wall crossing formulas
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abstract
In this paper we set up the family Seiberg-Witten theory. It can be applied to the counting of nodal pseudo-holomorphic curves in a symplectic 4-manifold (especially a Kahler surface). A new feature in this theory is that the chamber structure plays a more prominent role. We derive some wall crossing formulas measuring how the family Seiberg-Witten invariants change from one chamber to another.
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Family Seiberg-Witten equation on Kahler surface and $\pi_i(\Symp)$ on multiple-point blow ups of Calabi-Yau surfaces
Infinite generation of some higher homotopy groups of symplectomorphism groups is proved for n-point Kahler blowups of tori, K3 surfaces, and Enriques surfaces with non-resonant Kahler classes.