Stable curves and screens on fatgraphs
Geometric Topology
2007-07-11 v2 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.0707.1468,
title = {Stable curves and screens on fatgraphs},
author = {R. C. Penner and Greg McShane},
journal= {arXiv preprint arXiv:0707.1468},
year = {2007}
}
Comments
23 pages, 4 figures