02455nam a22003495a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400220018410000310020624500970023726000820033430000340041633600260045033700260047633800360050234700240053849000390056250600660060152012410066765000310190865000280193965000380196785600320200585600680203786-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20080901sz fot ||| 0|eng d a978303719548270a10.4171/0482doi ach0018173 7aPBPD2bicssc a55-xxa57-xx2msc1 atom Dieck, Tammo,eauthor.10aAlgebraic Topologyh[electronic resource] :bCorrected 2nd printing, 2010 /cTammo tom Dieck3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (578 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php 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.07aAlgebraic topology2bicssc07aAlgebraic topology2msc07aManifolds and cell complexes2msc40uhttps://doi.org/10.4171/048423cover imageuhttps://www.ems-ph.org/img/books/tomDieck_mini.jpg