Rectifying partial algebras over operads of complexes

Abstract

Kriz and May (1995) [2] introduced partial algebras over an operad. In this paper we prove that, in the category of chain complexes, partial algebras can be functorially replaced by quasi-isomorphic algebras. In particular, partial algebras contain all of the important homological and homotopical information that genuine algebras do. Applying this result to McClure's partial algebra in McClure (2006) [5] shows that the chains of a PL-manifold are quasi-isomorphic to an E ∞ -algebra.