English

Superforms, Tropical Cohomology, and Poincar\'e Duality

Algebraic Geometry 2018-03-28 v3

Abstract

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.

Keywords

Cite

@article{arxiv.1512.07409,
  title  = {Superforms, Tropical Cohomology, and Poincar\'e Duality},
  author = {Philipp Jell and Kristin Shaw and Jascha Smacka},
  journal= {arXiv preprint arXiv:1512.07409},
  year   = {2018}
}

Comments

32 pages. correction to signs in Section 4

R2 v1 2026-06-22T12:16:34.227Z