\(\Gamma\)-homology, topological André-Quillen homology and stabilization
The authors describe and compare three different homology constructions related to \(E_\infty\)-algebras: the \(\Gamma\)-homology, \(H_*^\Gamma\), of Robinson and Whitehouse, the topological André-Quillen homology, \(H_*^Q\), and the stabilization. They prove that the constructions agree when specialized to commutative rings. In particular, let \(k\) be a commutative ring, \(A\) be a commutative \(k\)-algebra, and \(Hk\) and \(HA\) be the corresponding Eilenberg-MacLane cofibrant commutative simplicial algebras, then there is an isomorphism of graded groups \(H_*^\Gamma(A/k;A)= H_*^Q (HA/Hk;HA)\).
scientific article; zbMATH DE number 1787544