附註:Includes bibliographical references (pages 457-462) and index.
Cover -- Preface -- Table of Contents -- Introduction -- Basic Concepts and Notation -- 1. Function Spaces -- 2. Connectedness and Algebraic Invariants -- 3. Homotopy groups -- 4. Homotopy Extension and Lifting Properties -- 5. CW-Complexes and Homology -- 6. Homotopy Properties of CW-Complexes -- 7. Cohomology Groups and Related Topics -- 8. Vector Bundles -- 9. K-Theory -- 10. Adams Operations and Applications -- 11. Relations Between Cohomology and Vector Bundles -- 12. Cohomology Theories and Brown Representability -- Appendix A -- Proof of the Dold-Thom Theorem -- Appendix B -- Proof of the Bott Periodicity Theorem -- References -- Symbols.
摘要:"The purpose of this book is to introduce algebraic topology using the novel approach of homotopy theory, an approach with clear applications in algebraic geometry as understood by Lawson and Voevodsky. This method allows the authors to cover the material more efficiently than the more common method using homological algebra. The basic concepts of homotopy theory, such as fibrations and cofibrations, are used to construct singular homology and cohomology, as well as K-theory. Throughout the text many other fundamental concepts are introduced, including the construction of the characteristic classes of vector bundles. Although functors appear constantly throughout the book, no previous knowledge about category theory is expected from the reader. This book is intended for advanced undergraduate and graduate students with a basic background in point set topology as well as group theory and can be used in a two-semester course."--Jacket.
