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Superforms, tropical cohomology, and Poincaré duality

Jell, Philipp ; Shaw, Kristin ; Smacka, Jascha


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

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