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.
|Original language||English (US)|
|Number of pages||43|
|Journal||Journal of Differential Geometry|
|State||Published - 2010|
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Geometry and Topology