Algebraic topology
Subtitle: Corrected 2nd printing, 2010
By: Tammo tom Dieck
Contributors: Tom Dieck, Tammo, author
Series: EMS Textbooks in Mathematics (ETB); EMS textbooks in mathematics
Publisher: European Mathematical Society Publishing House
Published: 2010
Place of publication: Zürich, Switzerland
Language: eng
Number of pages: 578
ISBN-13: 9783037195482
Subjects: Algebraic topology; Homotopy theory; Homology theory; Topologie algébrique; Homotopie; Homologie; Manifolds and cell complexes
Description: 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 to start 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 (masters) students to basic tools, concepts and results of algebraic topology. Sufficient background material from geometry and algebra is included.