Stable curves and screens on fatgraphs

R. C. Penner; Greg McShane

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arXiv · 0707.1468

Stable curves and screens on fatgraphs

R. C. Penner·Greg McShane

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Abstract

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.

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BibTeX RIS

R. C. Penner, Greg McShane. 2007-07-10. Stable curves and screens on fatgraphs. https://arxiv.org/abs/0707.1468

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