LEADER 02655nam 22004815a 450 001 9910151933803321 005 20220701125811.0 010 $a9783037190487 010 $a3-03719-548-7 024 70$a10.4171/048 035 $a(CKB)3710000000953837 035 $a(CH-001817-3)86-091109 035 $a(PPN)178155470 035 $a(EXLCZ)993710000000953837 100 $a20091109j20080901 fy 0 101 0 $aeng 135 $aurnn#mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAlgebraic topology /$fTammo tom Dieck 210 1$aZürich, Switzerland :$cEuropean Mathematical Society,$d[2008] 210 4$dİ2008 215 $a1 online resource (578 pages) 225 1 $aEMS Textbooks in Mathematics 300 $aCorrected 2nd printing, 2010 330 $aThis book is written as a textbook on algebraic topology. The first part covers the material for two introductory courses about homotopy and homology. The second part presents more advanced applications and concepts (duality, characteristic classes, homotopy groups of spheres, bordism). The author recommends to start an introductory course with homotopy theory. For this purpose, classical results are presented with new elementary proofs. Alternatively, one could start more traditionally with singular and axiomatic homology. Additional chapters are devoted to the geometry of manifolds, cell complexes and fibre bundles. A special feature is the rich supply of nearly 500 exercises and problems. Several sections include topics which have not appeared before in textbooks as well as simplified proofs for some important results. Prerequisites are standard point set topology (as recalled in the first chapter), elementary algebraic notions (modules, tensor product), and some terminology from category theory. The aim of the book is to introduce advanced undergraduate and graduate (masters) students to basic tools, concepts and results of algebraic topology. Sufficient background material from geometry and algebra is included. 410 0$aEMS textbooks in mathematics 606 $aTopologia algebraica$2lemac 606 $aAlgebraic topology$2bicssc 606 $aAlgebraic topology$2msc 606 $aManifolds and cell complexes$2msc 615 7$aTopologia algebraica. 615 07$aAlgebraic topology 615 07$aAlgebraic topology 615 07$aManifolds and cell complexes 686 $a55-xx$a57-xx$2msc 700 $aDieck$b Tammo tom$056647 801 0$bch0018173 906 $aBOOK 912 $a9910151933803321 996 $aAlgebraic topology$9229161 997 $aUNINA