Stable curves and screens on fatgraphs

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.

23 pages, 4 figures

References in corpus (3)

• Combinatorial Miller-Morita-Mumford classes and Witten cycles
• Probing mapping class groups using arcs
• Cluster algebras and Weil-Petersson forms

Cited by in corpus (5)

• Homology of the curve complex and the Steinberg module of the mapping class group
• Models of discretized moduli spaces, cohomological field theories, and Gaussian means
• On bases of tropical Plücker functions
• Extension of the Weil-Petersson connection
• Riemann surfaces with boundary and natural triangulations of the Teichmueller space