Cosimplicial C-infinity rings and the de Rham complex of Euclidean space

Abstract

A C-infinity ring is a set equipped with n-ary operations corresponding to smooth n-ary functions on the real line (satisfying natural axioms). We prove that the cosimplicial abelian group associated to the de Rham complex of Euclidean space has the structure of a cosimplicial C-infinity ring. We also analyse the notion of R-module (following Quillen) for a (co-)simplicial C-infinity ring R.