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Spin symplectic 4-manifolds near Bogomolov-Miyaoka-Yau line. (English) Zbl 1267.57034

Summary: We construct the first known family of simply connected spin symplectic 4-manifolds \(M_{k}\) satisfying \(c_{1}^{2}(M_{k}) / \chi _{h}(M_{k}) \to 9\) as \(k \to \infty \). Using \(M_{k}\), we also construct many other new spin symplectic 4-manifolds with nonnegative signature.

MSC:

57R55 Differentiable structures in differential topology
57R17 Symplectic and contact topology in high or arbitrary dimension
57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
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