Stable curves and screens on fatgraphs

Details Stable curves and screens on fatgraphs Stable curves and screens on fatgraphs

2007-07-10

arxiv.org/abs/0707.1468v2

Mathematics

Geometric Topology

23 pages, 4 figures

Scientific paper

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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