Journal of Differential Geometry
- J. Differential Geom.
- Volume 85, Number 1 (2010), 73-116.
Simple loops on surfaces and their intersection numbers
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.
J. Differential Geom., Volume 85, Number 1 (2010), 73-116.
First available in Project Euclid: 15 September 2010
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Luo, Feng. Simple loops on surfaces and their intersection numbers. J. Differential Geom. 85 (2010), no. 1, 73--116. doi:10.4310/jdg/1284557926. https://projecteuclid.org/euclid.jdg/1284557926