Superforms, Tropical Cohomology, and Poincaré Duality

23 Dec 2015 · Philipp Jell, Kristin Shaw, Jascha Smacka ·

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