Double pants decompositions of 2-surfaces

A pants decomposition of a 2-surface S is a maximal set of mutually non-intersecting closed curves on S whose complement is a union of "pants" (i.e. spheres with 3 holes). A double pants decomposition is a union of two pants decompositions of S. We define a remarkable class DP of double pants decompositions which we call "admissible", as well as a natural class T of transformations acting on double pants decompositions. We show that the transformations from T act transitively on the set of admissible double pants decompositions. These transformations also generate a group of automorphisms of DP, in particular, T contains the modular group. The work is joined with S. Natanzon.