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 EMS Textbooks in Mathematics 2008; 578 pp; hardcover Volume: 8 ISBN-10: 3-03719-048-5 ISBN-13: 978-3-03719-048-7 List Price: US$78 Member Price: US$62.40 Order Code: EMSTEXT/8 This book is written as a textbook on algebraic topology. The first part covers the material for two introductory courses about homotopy and homology. The second part presents more advanced applications and concepts (duality, characteristic classes, homotopy groups of spheres, bordism). The author recommends starting an introductory course with homotopy theory. For this purpose, classical results are presented with new elementary proofs. Alternatively, one could start more traditionally with singular and axiomatic homology. Additional chapters are devoted to the geometry of manifolds, cell complexes and fibre bundles. A special feature is the rich supply of nearly 500 exercises and problems. Several sections include topics which have not appeared before in textbooks as well as simplified proofs for some important results. Prerequisites are standard point set topology (as recalled in the first chapter), elementary algebraic notions (modules, tensor product), and some terminology from category theory. The aim of the book is to introduce advanced undergraduate and graduate (master's) students to basic tools, concepts and results of algebraic topology. Sufficient background material from geometry and algebra is included. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. Readership Advanced undergraduates and graduate students interested in algebraic topology. Table of Contents Topological spaces The fundamental group Covering spaces Elementary homotopy theory Cofibrations and fibrations Homotopy groups Stable homotopy. Duality Cell complexes Singular homology Homology Homological algebra Cellular homology Partitions of unity in homotopy theory Bundles Manifolds Homology of manifolds Cohomology Duality Characteristic classes Homology and homotopy Bordism Bibliography Symbols Index