Journal of Differential Geometry

Simple loops on surfaces and their intersection numbers

Feng Luo

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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 Teichmüller 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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J. Differential Geom., Volume 85, Number 1 (2010), 73-116.

First available in Project Euclid: 15 September 2010

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Luo, Feng. Simple loops on surfaces and their intersection numbers. J. Differential Geom. 85 (2010), no. 1, 73--116. doi:10.4310/jdg/1284557926.

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