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Tropical contractions to integral affine manifolds with singularities

We construct contraction maps from tropical Calabi--Yau varieties to the integral affine manifolds with singularities that arise as the dual intersection complexes of toric degenerations of Calabi--Yau varieties in the Gross--Siebert program. We show that the contractions preserve tropical cohomology groups, and send the eigenwaves to the radiance obstructions. As an application, we also prove the Poincar\'{e}--Verdier duality for integral affine manifolds with singularities.