# Algebraic Topology

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*Tammo tom Dieck*

A publication of the European Mathematical Society

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.