Algebraic Topology

Tammo Tom Dieck (Autor)

Buch | Hardcover

XI, 567 Seiten

2008 | 1., Aufl.
EMS Press (Verlag)
978-3-03719-048-7 (ISBN)

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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.

Erscheint lt. Verlag	1.9.2008
Reihe/Serie	EMS Textbooks in Mathematics
Sprache	englisch
Maße	165 x 235 mm
Gewicht	1184 g
Einbandart	gebunden
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	cell complexes • cofibrations • Covering spaces • fibrations • HC/Mathematik • homotopy groups • Mathematik • smooth • Vector Bundles
ISBN-10	3-03719-048-5 / 3037190485
ISBN-13	978-3-03719-048-7 / 9783037190487
Zustand	Neuware