Split dual Dyer-Lashof operations Original Research Article

For each admissible monomial of Dyer-Lashof operations QI, we define a corresponding natural function image, called a Dyer-Lashof splitting. For every homogeneous class x in H*(X), a Dyer-Lashof splitting image determines a canonical element y in H*(ΩnεnX) so that y is connected to x by the dual homomorphism to the operation QI. The sum of the images of all the admissible Dyer-Lashof splittings contains a complete set of algebra generators for H*(ΩnΣnX).