The mod 2 homology of free spectral Lie algebras

Abstract

The Goodwillie derivatives of the identity functor on pointed spaces form an operad ∂ ∗ ( I d ) \partial _\ast (\mathrm {Id}) in spectra. Adapting a definition of Behrens, we introduce mod 2 2 homology operations for algebras over this operad and prove that these operations account for all the mod 2 2 homology of free algebras on suspension spectra of simply connected spaces.