English

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

R2 v1 2026-06-21T08:56:55.417Z