Tropical lambda lengths, measured laminations and convexity

R. C. Penner Aarhus University

Differential Geometry mathscidoc:1609.10317

Journal of Differential Geometry, 94, (2), 343-365, 2013
This work uncovers the tropical analogue, for measured laminations, of the convex hull construction in decorated Teichm¨uller theory; namely, it is a study in coordinates of geometric degeneration to a point of Thurston’s boundary for Teichm¨uller space. This may offer a paradigm for the extension of the basic cell decomposition of Riemann’s moduli space to other contexts for general moduli spaces of flat connections on a surface. In any case, this discussion drastically simplifies aspects of previous related studies as is explained. Furthermore, a new class of measured laminations relative to an ideal cell decomposition of a surface is discovered in the limit. Finally, the tropical analogue of the convex hull construction inMinkowski space is formulated as an explicit algorithm that serially simplifies a triangulation with respect to a fixed lamination and has its own independent interest.
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@inproceedings{r.2013tropical,
  title={TROPICAL LAMBDA LENGTHS, MEASURED LAMINATIONS AND CONVEXITY},
  author={R. C. Penner},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914080449030440979},
  booktitle={Journal of Differential Geometry},
  volume={94},
  number={2},
  pages={343-365},
  year={2013},
}
R. C. Penner. TROPICAL LAMBDA LENGTHS, MEASURED LAMINATIONS AND CONVEXITY. 2013. Vol. 94. In Journal of Differential Geometry. pp.343-365. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914080449030440979.
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