The Goodwillie derivatives of the identity functor on pointed spaces form an operad in spectra. Adapting a definition of Behrens, we introduce mod 2 homology operations for algebras over this operad and prove these operations account for all the mod 2 homology of free algebras on suspension spectra of simply-connected spaces.
In the upcoming paper @cite_5 , Brantner computes the @math -homology of certain free @math -algebras in the category of @math -local spectra and thus computes the @math -homology operations on @math -local @math -algebras. Here @math and @math denote Morava @math -theory and Morava @math -theory respectively.
@cite_5
1541776832
CW-complexes generalities on homotopy classes of mappings homotopy groups homotopy theory of CW-complexes homotopy with local coefficients homology of fibre spaces elementary theory the homology suspension Postnikov systems on mappings into group-like spaces homotopy operations stable homotopy and homology homology of fibre spaces compact Lie groups additive relations.