What is in this book and what is not

The purpose of this book is to present those techniques of algebraic topology which are needed in the presentation of the results on the exponents of homotopy groups which were proven by Cohen, Moore, and the author. It was decided that all of the details of those techniques would be completely and honestly presented.

Homotopy groups with coefficients are fundamental to the whole enterprise and have and will be useful in other things. The 2-primary theory was not excluded but the fact that certain things are just not true for the 2-primary case reinforces the eventual restriction, more and more, to the odd primary case and finally to the case of primes greater than 3. The argument could have been made that the exact sequences of these groups related to pairs and to fibrations are all a consequence of the fundamental work of Barratt and of Puppe on cofibration sequences and can be found as a special case in the books of G. Whitehead or of E. H. Spanier. But the general theory does not handle the low dimensional cases which correspond to the fundamental group and the only way to provide an honest uniform treatment was to present the whole theory in detail. So that is what is done.

Localization has undergone a revolution in the hands of Dror Farjoun and of Bousfield. This new theory is incredibly general.