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

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. The appendix containing essential facts on model categories, the numerous examples and the suggestions for further reading make this a friendly introduction to an often daunting subject. "The aim of this book is to be an accessible introduction to stable homotopy theory that novices, particularly graduate students, can use to learn the fundamentals of the subject. For the experts we hope to have provided a useful compendium of results across the main areas of stable homotopy theory. This book is not intended to replace any specific part of the existing literature, but instead to give a smoother, more coherent introduction to stable homotopy theory. We use modern techniques to give a streamlined development that avoids a number of outdated, and often over-complicated, constructions of a suitable stable homotopy category. We cover the most pressing topics for a novice and give a narrative to motivate the development. This narrative is missing from much of the current literature, which often assumes the reader already knows stable homotopy theory and hence understands why any given definition or result is important. The majority of sections have been written to (hopefully) contain all details required for a graduate student. The remaining sections are intended to give an overview of more specialised or advanced topics, with references to the central texts for those areas. It is hoped that once the reader has read the chapters relevant to their research, they will be well-prepared to dive into the rest of the literature, and to know what to read next"-- Provided by publisher A Comprehensive Introduction To Stable Homotopy Theory For Beginning Graduate Students, From Motivating Phenomena To Current Research.