Аннотация:
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.