%0 Journal Article
%T Stable curves and screens on fatgraphs
%A R. C. Penner
%A Greg McShane
%J Mathematics
%D 2007
%I arXiv
%X 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.
%U http://arxiv.org/abs/0707.1468v2