
Let \(X\) be a closed smooth four-manifold which is homotopy equivalent to a K3 surface. Let \(P\to X\) be the unique \(\text{Spin}^c\)-structure up to isomorphism with trivial determinant line bundle. Then the value of the Seiberg-Witten invariant of \(P\) is congruent to one modulo two.
4-manifold, \(\text{Spin}^ c\)-structure, Topology of the Euclidean \(4\)-space, \(4\)-manifolds, K3 surface, Seiberg-Witten invariant
4-manifold, \(\text{Spin}^ c\)-structure, Topology of the Euclidean \(4\)-space, \(4\)-manifolds, K3 surface, Seiberg-Witten invariant
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