Cycle matroids of graphings: from convergence to duality

As a continuation of our work on the quotient-convergence of submodular setfunctions, in the paper Cycle Matroids of Graphings: From Convergence to Duality, we study the connection between local-global convergence of graphs and quotient-convergence of their cycle matroids. We characterize the exposed points of the associated convex set, forming an analytic counterpart of matroid base-polytopes. Finally, we consider dual planar graphings and show that the cycle matroid of one is the cocycle matroid of its dual if and only if the underlying graphings are hyperfinite.