Stable curves and screens on fatgraphs

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Penner, R. C.
McShane, Greg
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Abstract
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The mapping class group invariant ideal cell decomposition of the Teichmueller space of a punctured surface times an open simplex has been used in a number of computations. This paper answers a question about the asymptotics of this decomposition, namely, in a given cell of the decomposition, which curves can be short? Screens are a new combinatorial structure which provide an answer to this question. The heart of the calculation here involves Ptolemy transformations and the triangle inequalities on lambda lengths.
Comment: 23 pages, 4 figures
Keywords
Mathematics - Geometric Topology, Mathematics - Algebraic Geometry, 32G15, 57M99, 14H10, 14G15, 57N05, 20F99
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