A sheaf-theoretic approach to tropical homology
Algebraic Geometry
2019-06-24 v1 Combinatorics
Abstract
We introduce a sheaf-theoretic approach to tropical homology, especially for tropical homology with potentially non-compact supports. Our setup is suited to study the functorial properties of tropical homology, and we show that it behaves analogously to classical Borel-Moore homology in the sense that there are proper push-forwards, cross products, and cup products with tropical cohomology classes, and that it satisfies identities like the projection formula and the K\"unneth theorem. Our framework allows for a natural definition of the tropical cycle class map, which we show to be a natural transformation. Finally, we prove Poincar\'e-Verdier duality over the integers on tropical manifolds.
Keywords
Cite
@article{arxiv.1906.09245,
title = {A sheaf-theoretic approach to tropical homology},
author = {Andreas Gross and Farbod Shokrieh},
journal= {arXiv preprint arXiv:1906.09245},
year = {2019}
}