On the E2 structure of cochains

Abstract

Let R be a ring containing 1/m for m < p. Let A be an E₃ algebra over R concentrated in the degree range r + 1 ≤ n ≤ rp − p + 1. Then, as an E ₂ algebra, A is equivalent to a commutative algebra. As a consequence, if X is an r connected, rp − p + 1 dimensional, finite simplicial set, then S^*(X, R), the singular cochain complex over the ring R, is equivalent as an E₂ algebra to a commutative algebra.