A closed symplectic manifold of real dimension four cannot be a connected sum of two oriented smooth four-manifolds each with positive positive index of the intersection form. The total exceeds one; Taubes nonvanishing theorem and connected-sum vanishing of the Seiberg–Witten invariant would force the same invariant to be both nonzero and zero.

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  1. Taubes nonvanishing theorem
  2. Seiberg–Witten invariant of a four-manifold
  3. Smooth four-manifold
  4. 4-manifold
  5. Topological manifold
  6. Topology
  7. Geometry and topology
  8. Area of mathematics
  9. Mathematics
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