Steenrod operations on the negative cyclic homology of the shc-cochain algebras

Abstract

In this paper we prove that the Steenrod operations act naturally on the negative cyclic homology of a differential graded algebra A over the prime field F p satisfying some extra conditions. When A denotes the singular cochains with coefficients in F p of a 1-connected space X, these extra conditions are satisfied. The Jones isomorphism identifies these Steenrod operations with the usual ones on the S 1 -equivariant cohomology of the free loop space on X with coefficients in F p . We conclude by performing some calculations on the negative cyclic homology.