دانلود کتاب Algebraic topology from a homotopical viewpoint

This clear exposition of the flourishing field of fixed point theory, an important tool in the fields of differential equations and functional equations, starts from the basics of Banach's contraction theorem and develops most of the main results and techniques. The book explores many applications of the theory to analysis, with topological considerations playing a crucial role. The very extensive bibliography and close to 100 exercises mean that it can be used both as a text and as a comprehensive reference work, currently the only one of its type "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.  Read more... 1. Functions 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 -- App. A. Proof of the Dold-Thom Theorem -- App. B. Proof of the Bott Periodicity Theorem