On the Teichmüller tower of mapping class groups

By A. Hatcher, P. Lochak, Leila Schneps. 2000

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The Weil-Petersson metric and volumes of 3-dimensional hyperbolic convex cores (2001, background): “The pants graph is the 1-skeleton of the pants complex, introduced in [HT] (see also [ HLS ]) which is there proven to be connected.”
Tameness of hyperbolic 3-manifolds (2004, background): “A theorem of Hatcher, Lochak, and Schneps [33] implies that the pants complex is connected.”
On a subgroup of the Grothendieck-Teichmüller group acting on the tower of profinite Teichmüller modular groups (2000, methodology): “Starting from a quilt Q/P ,w e def ine an action of IΓ on all (infinitely many) Dehn twists in ˆ Γ(Σ) in well-defined manners (§8) by using the description of the simplicial complex of pants decompositions given in [ HLS ].”
Automorphisms of the pants complex (2004, background): “Hatcher, Lochak, and Schneps gave the pants complex its present form, and, in particular, they showed that it is connected and simply connected (see [4]).”