Screen LibraryFoundations of stable homotopy theory /
"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 th...
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| Main Authors: | |
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| Group Author: | |
| Published: |
Cambridge University Press,
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| Publisher Address: | Cambridge, United Kingdom : |
| Publication Dates: | 2020. |
| Literature type: | Book |
| Language: | English |
| Series: |
Cambridge studies in advanced mathematics ;
185 |
| Subjects: | |
| Summary: |
"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 We use modern techniques to give a streamlined development that avoids a number of outdated, and often over-complicated, constructions of a suitable stable homotopy category.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"-- |
| Carrier Form: | vi, 423 pages : illustrations ; 24 cm. |
| Bibliography: | Includes bibliographical references (pages 411-417) and index. |
| ISBN: |
9781108482783 1108482783 |
| Index Number: | QA612 |
| CLC: | O189.23 |
| Call Number: | O189.23/B261 |
| Contents: | Introduction -- Basics of stable homotopy theory -- Sequential spectra and the stable homotopy category -- The suspension and loop functors -- Triangulated categories -- Modern categories of spectra -- Monoidal structures -- Left bousfield localisation -- Model categories. |