Superforms, tropical cohomology, and Poincaré duality

By Philipp Jell, Kristin M. Shaw, Jascha Smacka. Advances in Geometry, 2015

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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.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ff983600df100978c33fca578ec28b7f11e89480