 

Harold Sultan
Separating pants decompositions in the pants complex view print


Published: 
March 5, 2012 
Keywords: 
Pants complex, Teichmüller space, Separating curves, loglength connected graphs 
Subject: 
Primary: 20F65, 30F60; Secondary: 57M15 


Abstract
We study the topological types of pants decompositions of a surface by associating to any pants decomposition P, its pants
decomposition graph, Γ(P). This perspective provides a convenient way to analyze the maximum distance in the pants complex
of any pants decomposition to a pants decomposition containing a nontrivial separating curve for all surfaces of finite type. We
provide an asymptotically sharp approximation of this nontrivial distance in terms of the topology of the surface. In particular,
for closed surfaces of genus g we show the maximum distance in the pants complex of any pants decomposition to a pants
decomposition containing a separating curve grows asymptotically like the function log(g). The lower bounds follow from an
explicit constructive algorithm for an infinite family of high girth loglength connected graphs, which may be of independent
interest.


Author information
Department of Mathematics, Columbia University, New York, NY 10027
HSultan@math.columbia.edu

