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Given a compact orientable surface, we determine a complete set of relations for a function defined on the set of all homotopy classes of simple loops to be a geometric intersection number function. As a consequence, Thurston’s space of measured laminations and Thurston’s compactification of the Teichm¨uller space are described by a set of explicit equations. These equations are polynomials in the max-plus semi-ring structure on the real numbers. It shows that Thurston’s theory of measured laminations is within the domain of tropical geometry.

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