Foundations of stable homotopy theory /

The stated goal of the authors is to provide an accessible entry point to stable homotopy theory for first-year graduate students. The necessary prerequisites are good undergraduate knowledge of point-set topology and algebraic topology. Barnes (Queens Univ., Belfast) and Roitzheim (Univ. of Kent) achieve their goal within the first three chapters by discussing a large collection of examples. Included among them are the Spanier-Whitehead category, sequential spectra, the stable homotopy category, and two important functors, namely the suspension and the loop functors. After this point, the pace of the treatment quickens as the authors cover triangulated categories (chapter 4), modern categories of spectra (chapter 5), monoidal structures (chapter 6), and left Bousfield localizations (chapter 7). There are no exercises in the book, which makes both self-study and the assignment of homework sets difficult. For this reason alone, it seems likely that the primary use of the book will be as a reference source. Summing Up: Optional. Graduate students, faculty, and researchers. --Miklos Bona, University of Florida