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Homotopy \(K3\)’s with several symplectic structures. (English) Zbl 1067.57031
The main result states that for each integer \(n\), there is a homotopy \(K3\) smooth 4-manifold that admits \(n\) inequivalent symplectic structures. The construction of the manifold uses a generalization of the Fintushel-Stern link surgery, and the symplectic structures are distinguished by comparing their canonical classes.

MSC:
57R57 Applications of global analysis to structures on manifolds
57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
57R17 Symplectic and contact topology in high or arbitrary dimension
57N13 Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010)
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