Superforms, Tropical Cohomology, and Poincaré Duality

Abstract

We establish a canonical isomorphism between two bigraded cohomology theories for polyhedral spaces: Dolbeault cohomology of superforms and tropical cohomology. Furthermore, we prove Poincaré duality for cohomology of tropical manifolds, which are polyhedral spaces locally given by Bergman fans of matroids.

32 pages. correction to signs in Section 4