Higher homotopy commutativity and the resultohedra

Abstract

We define a higher homotopy commutativity for the multiplication of a topological monoid. To give the definition, we use the resultohedra constructed by Gelfand, Kapranov and Zelevinsky. Using the higher homotopy commutativity, we have necessary and sufficient conditions for the classifying space of a topological monoid to have a special structure considered by Félix, Tanré and Aguadé. It is also shown that our higher homotopy commutativity is rationally equivalent to the one of Williams.