The multifacettes of the Stasheff polytope

The Stasheff complex is a polytope whose vertices are in bijection with the planar binary trees (one polytope for each n). It plays a role in many problems in algebraic topology (loop spaces, compactification). Recently it appeared also in algebraic combinatorics and in noncommutative geometry. In this lecture I will present a simple construction of these polytopes and show that the minimal triangulation is related to the "parking functions". Wspólne posiedzenie seminarium z Topologii Algebraicznej i seminarium z Geometrii Nieprzemiennej.