Algebraic Topology from a Homotopical Viewpoint

Function Spaces.- Connectedness and Algebraic Invariants.- Homotopy groups.- Homotopy Extension and Lifting Properties.- CW-Complexes and Homology.- Homotopy Properties of CW-Complexes.- Cohomology Groups and Related Topics.- Vector Bundles.- K-Theory.- Adams Operations and Applications.- Relations Between Cohomology and Vector Bundles.- Cohomology Theories and Brown Representability.

From the reviews:"This is a basic course on algebraic topology and … it is excellently written and composed and can be strongly recommended to anybody wishing to learn the field. The reader can find many examples, calculations, and also a number of exercises. … The book has two appendices, … references consisting of 83 items and a long list of symbols. There are many remarks and comments making the orientation of the reader in the field of algebraic topology easier … ." (EMS, June, 2004)"The modus operandi of algebraic topology is to associate algebraic invariants, such as groups or rings, to a topological space in such a way that equivalent spaces exhibit isomorphic invariants; here, ‘equivalent’ may be chosen to fit the geometry of the problem. In this book, ‘equivalent’ means homotopy equivalent … . For its clarity and directness, a welcome addition to advanced mathematics collections. Upper-division undergraduates through faculty." (J. McCleary, CHOICE, December, 2002)"The purpose of this book is to introduce algebraic topology using the novel approach of homotopy theory … . The basic concepts of homotopy theory … are used to construct singular homology and cohomology, as well as K-theory. … Throughout the text many other fundamental concepts are introduced … ." (L’Enseignement Mathematique, Vol. 48 (3-4), 2002)“The book of Aguilar, Gitler and Prieto gives an interesting new approach for a first course in algebraic topology. … What is also very interesting is the fact that the book contains a detailed presentation of some deep results of algebraic topology not usually covered by a first book in algebraic topology … . The text is carefully well written. … the student in algebraic topology will find in the book a lot of interesting well-exposed material.” (Yves Félix, Bulletin of the Belgian Mathematical Society, 2007)