Special Lagrangian Cycles and Calabi-Yau Transitions

We construct special Lagrangian 3-spheres in non-Kähler compact threefolds equipped with the Fu-Li-Yau geometry. These nonKähler geometries emerge from topological transitions of compact CalabiYau threefolds. From this point of view, a conifold transition exchanges holomorphic 2-cycles for special Lagrangian 3-cycles.

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