The Orlik-Solomon Algebra and the Bergman Fan of a Matroid

Abstract: Given a matroid $M$ one can define its Orlik-Solomon algebra $OS(M)$ and the Bergman fan $\Sigma_0(M)$. On the other hand to any rational polyhedral fan $\Sigma$ one can associate its tropical homology and cohomology groups $\F_\bullet(\Sigma)$, $\F^\bullet (\Sigma)$. We will show that the projective Orlik-Solomon algebra $OS_0(M)$ is canonically isomorphic to $\F^\bullet (\Sigma_0(M))$.