Cycles, cocycles, and duality on tropical manifolds

Abstract

We prove a Poincaré duality for the Chow rings of smooth fans whose support are tropical linear spaces. As a consequence, we show that cycles and cocycles on tropical manifolds are Poincaré dual to each other. This allows us to define pull-backs of tropical cycles along arbitrary morphisms with smooth target.

Final version. To appear in the Proceedings of the AMS