  We consider collections of disjoint simple closed curves in a compact
orientable surface which decompose the surface into pairs of pants. The isotopy
classes of such curve systems form the vertices of a 2-complex, whose edges
correspond to certain simple moves in which only one curve changes, and whose
2-cells correspond to certain elementary cycles of simple moves. The main
theorem is that this 2-complex is simply-connected. Thus any two pants
decompositions of a surface are joinable by a sequence of simple moves, and any
two such sequences of simple move are related by the elementary relations. The
proof is similar to the proof, in a 1980 paper with W. Thurston, of an
analogous result for curve systems with connected genus zero complement. [The
present paper is essentially an excerpt from a joint paper with P. Lochak and
L. Schneps which is to appear in Crelle's Journal.]
