Open Access
June 2013 Tropical Lambda Lengths, Measured Laminations and Convexity
R. C. Penner
J. Differential Geom. 94(2): 343-365 (June 2013). DOI: 10.4310/jdg/1367438652


This work uncovers the tropical analogue, for measured laminations, of the convex hull construction in decorated Teichmüller theory; namely, it is a study in coordinates of geometric degeneration to a point of Thurston’s boundary for Teichmüller 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 in Minkowski 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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R. C. Penner. "Tropical Lambda Lengths, Measured Laminations and Convexity." J. Differential Geom. 94 (2) 343 - 365, June 2013.


Published: June 2013
First available in Project Euclid: 1 May 2013

zbMATH: 1276.30057
MathSciNet: MR3080485
Digital Object Identifier: 10.4310/jdg/1367438652

Rights: Copyright © 2013 Lehigh University

Vol.94 • No. 2 • June 2013
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