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 Fp satisfying some extra conditions. When A denotes the singular cochains with coefficients in Fp of a 1-connected space X, these extra conditions are satisfied. The Jones isomorphism identifies these Steenrod operations with the usual ones on the S1-equivariant cohomology of the free loop space on X with coefficients in Fp. We conclude by performing some calculations on the negative cyclic homology.
Homology, Homotopy and Applications, Vol. 11 (2009), No. 1, pp.315-348.
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