Cocycles on tropical varieties via piecewise polynomials

We use piecewise polynomials to define tropical cocycles generalising the well-known notion of tropical Cartier divisors to higher codimensions. Groups of cocycles are tropical analogues of Chow cohomology groups. We also introduce an intersection product of cocycles with tropical cycles - the counterpart of the classical cap product - and prove that this gives rise to a Poincaré duality in some cases.

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