02655nam 22004815a 450 991015193380332120220701125811.097830371904873-03719-548-710.4171/048(CKB)3710000000953837(CH-001817-3)86-091109(PPN)178155470(EXLCZ)99371000000095383720091109j20080901 fy 0engurnn#mmmmamaatxtrdacontentcrdamediacrrdacarrierAlgebraic topology /Tammo tom DieckZürich, Switzerland :European Mathematical Society,[2008]©20081 online resource (578 pages)EMS Textbooks in MathematicsCorrected 2nd printing, 2010This 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.EMS textbooks in mathematicsTopologia algebraicalemacAlgebraic topologybicsscAlgebraic topologymscManifolds and cell complexesmscTopologia algebraica.Algebraic topologyAlgebraic topologyManifolds and cell complexes55-xx57-xxmscDieck Tammo tom56647ch0018173BOOK9910151933803321Algebraic topology229161UNINA