Foundations of Stable Homotopy Theory: 185 (Cambridge Studies in Advanced Mathematics, Series Number 185)

by David Barnes (Author), David Barnes (Author), Constanze Roitzheim (Author)

• New

  Hardcover
  2020

  $80.23

  The beginning graduate student in homotopy theory is confronted with a vast literature on spectra that is scattered across books, articles and decades. There is much folklore but very few easy entry points. This comprehensive introduction to stable homotopy theory changes that. It presents the foundations of the subject together in one place for the first time, from the motivating phenomena to the modern theory, at a level suitable for those with only a first course in algebraic topology. Starting from stable homotopy groups and (co)homology theories, the authors study the most important categories of spectra and the stable homotopy category, before moving on to computational aspects and more advanced topics such as monoidal structures, localisations and chromatic homotopy theory. An appendix containing the essential facts on model categories, and the many examples and suggestions for further reading make this is a friendly introduction to an often daunting subject.