Abstract. In this paper we construct a small E ∞ chain operad S which acts naturally on the normalized cochains S ∗ X of a topological space. We also construct, for each n, a suboperad Sn which is quasi-isomorphic to the normalized singular chains of the little n-cubes operad. The case n = 2 leads to a substantial simplification of our earlier proof of Deligne’s Hochschild cohomology conjecture. 1. Introduction. This paper has two goals. The first (see Theorem 2.15 and Remark 2.16(a)) is to construct a small E ∞ chain operad S which acts naturally on the normalized cochains S∗X of a topological space X. This is of interest in view of a theorem of Mandell [15, page 44] which states that if O is any E ∞ chain operad over Fp (the algebraic closure of the field with

Given a good homology theory E and a topological space X, E∗X is not just an E∗-module but also a comodule over the Hopf algebroid (E∗, E∗E). We establish a framework for studying the homological algebra of comodules over a well-behaved Hopf algebroid (A, Γ). That is, we construct

Abstract. We describe the author’s research with Neil Strickland on the global algebra and global homological algebra of the category of BP∗BP-