Taubes' simply connected symplectic decomposition conjecture

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Let XX be a smooth, compact, oriented, simply connected 44-manifold without boundary. A connected sum here means a decomposition into smooth four-manifolds, and both orientations of each symplectic summand are allowed. Taubes' simply connected decomposition conjecture. Every smooth, compact, oriented, simply connected four-manifold without boundary is a connected sum of symplectic manifolds, with both orientations allowed. This is a refinement of the preceding decomposition question restricted to simply connected four-manifolds. The source states that this conjecture remains open.

References

Primary source

M. Marcolli, “Notes on Seiberg-Witten Gauge Theory”, arXiv:dg-ga/9509005 (1995).

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