ABSTRACT
Let A be a topological space, and let t > 1. In Chapter 8 we define and examine a certain dga Όa associated to A and t , which we call the ring of stable homotopy operations under A. We may think of Oa = Οα [ϊ] as a simultaneous generalization, of the usual ring of stable mod px homotopy operations on one hand, and of iterated Whitehead or Samelson products on the other. There is a strong connection between Oa and ϋ/*(ΩΑ; Z^t), and we present some results and some open questions about this connection. The dga of stable homotopy operations will later provide the correct framework within which to understand and prove many of the important properties of our spaces D*.
