Abstract |
Given a matroid M one can define its Orlik-Solomon algebra OS(M)
and the Bergman fan Σ0(M). On the other hand to any rational polyhedral fan
Σ one can associate its tropical homology and cohomology groups
F•(Σ), F•(Σ).
We show that the projective Orlik-Solomon algebra OS0(M) is canonically isomorphic to
F•(Σ0(M)). In the realizable case this provides
a geometric interpretation of the homology of the complement of the corresponding hyperplane arrangement
in Pn.
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