Simple loops on surfaces and their intersection numbers

Feng Luo Rutgers University

Differential Geometry mathscidoc:1609.10178

Journal of Differential Geometry, 85, (1), 73-115, 2010
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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@inproceedings{feng2010simple,
  title={SIMPLE LOOPS ON SURFACES AND THEIR INTERSECTION NUMBERS},
  author={Feng Luo},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911214740871341835},
  booktitle={Journal of Differential Geometry},
  volume={85},
  number={1},
  pages={73-115},
  year={2010},
}
Feng Luo. SIMPLE LOOPS ON SURFACES AND THEIR INTERSECTION NUMBERS. 2010. Vol. 85. In Journal of Differential Geometry. pp.73-115. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911214740871341835.
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