Smooth fiber sum along unknotted null-homologous spheres
ID: smooth-fiber-sum-along-unknotted-null-homologous-spheres
For standard unknotted spheres contained in four-balls in and , the standard fiber-reversing gluing gives the displayed connected sum. The complement of an unknotted in is , and its double is . The portions of and outside the four-balls remain as connected summands. Taking both ambient manifolds to be the Complex projective plane gives a smooth fiber sum with no symplectic form, by the symplectic connected-sum obstruction.
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