نظریه هموتوپی، جلد هشتم (ریاضیات خالص و کاربردی)

The recognition of the branch of mathematics now known as homotopy theory occurred a few years after the introduction of homotopy groups by Witold Hurewicz in 1935. Since then, thanks to numerous advances by many researchers, it plays an increasingly important role in the expanding field of algebraic topology. This book is designed for the beginning student or newcomer to this branch of mathematics--who has a little knowledge of algebraic topology--to be introduced to the basic principles of homotopy theory. There is enough detail to provide a full understanding of the fundamental ideas and mastery of elementary techniques, which will hopefully lead to more advanced studies in the topic Front Cover; Homotopy Theory, Volume 8; Copyright Page; PREFACE; Contents; LIST OF SPECIAL SYMBOLS AND ABBREVIATIONS; CHAPTER I. MAIN PROBLEM AND PRELIMINARY NOTIONS; CHAPTER II. SOME SPECIAL CASES OF THE MAIN PROBLEMS; CHAPTER III. FIBER SPACES; CHAPTER IV. HOMOTOPY GROUPS; CHAPTER V. THE CALCULATION OF HOMOTOPY GROUPS; CHAPTER VI. OBSTRUCTION THEORY; CHAPTER VII. COHOMOTOPY GROUPS; CHAPTER VIII. EXACT COUPLES AND SPECTRAL SEQUENCES; CHAPTER IX. THE SPECTRALSEQUENCE OF A FIBER SPACE; CHAPTER X. CLASSES OF ABELIAN GROUPS; CHAPTER XI. HOMOTOPY GROUPS OF SPHERES; BIBLIOGRAPHY; INDEX.