Tropical varieties and integral affine manifolds with singularities

There are two types of spaces which we study in tropical geometry. One is tropical varieties which appear as the tropicalizations of algebraic varieties over a valuation field. The other one is integral affine manifolds with singularities which arise as the dual intersection complexes of toric degenerations in the Gross–Siebert program. In the talk, we discuss relations between these two different types of tropical spaces. We construct contraction maps from tropical Calabi–Yau varieties to corresponding integral affine manifolds with singularities, and show that they preserve tropical (co)homology groups and the invariants of tropical structures called eigenwaves/radiance obstructions.