ABSTRACT
In Chapter 9 we at last state the main theorem of this monograph, Theorem 9.1. It asserts the existence of the spaces {D k}k>o and of diagrams like (IK) (see (9C)) for each D k , and it outlines twelve of their major properties. The list of properties will be continued in Theorems 12.4 and 12.6. We examine in Chapter 9 what the theorem says at k — 0 and why it is true there. We detail how to perform the construction of Dk out of D k - 1-We get started on the proof of Theorem 9.1 by proving the three parts that provide descriptions of Adams-Hilton models. Theorem 9.1 is a herculean project: all of Chapters 9 through 13 will be needed in order to complete its proof.
