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Tropicalized Lambda Lengths, Measured Laminations and Convexity

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  • R. C. Penner, Denmark
This work uncovers the tropical analogue for measured laminations of the convex hull construction of decorated Teichmueller theory, namely, it is a study in coordinates of geometric degeneration to a point of Thurston's boundary for Teichmueller 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 applications.
Translated title of the contributionTropicalized Lambda Lengths, Measured Laminations and Convexity
Original languageEnglish
Number of pages23
Publication statusPublished - 14 Jun 2011

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