Open Access
May 2010 Simple loops on surfaces and their intersection numbers
Feng Luo
J. Differential Geom. 85(1): 73-116 (May 2010). DOI: 10.4310/jdg/1284557926


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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Feng Luo. "Simple loops on surfaces and their intersection numbers." J. Differential Geom. 85 (1) 73 - 116, May 2010.


Published: May 2010
First available in Project Euclid: 15 September 2010

zbMATH: 0906.57007
MathSciNet: MR2719409
Digital Object Identifier: 10.4310/jdg/1284557926

Rights: Copyright © 2010 Lehigh University

Vol.85 • No. 1 • May 2010
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