2007/07/10 by Penner, R. C., McShane, Greg · 2 citations
#14G15 #14H10 #20F99 #32G15 #57M99 #57N05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.0707.1468
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.