Mathematical Proceedings of the Cambridge Philosophical Society

Operads and Γ-homology of commutative rings

a1 Mathematics Institute, University of Warwick, Coventry CV4 7AL. e-mail:
a2 Laboratoire de Géométrie-Algèbre, Université d'Artois - Pôle de Lens, Rue Jean Souvraz, S.P. 18 - 62307 Lens, France. e-mail:


We introduce Γ-homology, the natural homology theory for E[infty infinity]-algebras, and a cyclic version of it. Γ-homology specializes to a new homology theory for discrete commutative rings, very different in general from André–Quillen homology. We prove its general properties, including at base change and transitivity theorems. We give an explicit bicomplex for the Γ-homology of a discrete algebra, and elucidate connections with stable homotopy theory.

(Received May 8 2000)
(Revised October 24 2000)


1 S.W. was supported by a TMR grant from the European Union, held at the Laboratoire d'Analyse, Géométrie et Applications (UMR 7539 au CNRS), Université Paris-Nord. A.R. was supported by the EU Homotopy Theory Network.