This is a book in pure mathematics dealing with homotopy theory, one of the main branches of algebraic topology. The principal topics are as follows: BasicHomotopy; H-spaces and co-H-spaces; fibrations and cofibrations; exact sequences of homotopy sets, actions, and coactions; homotopy pushouts and pullbacks;classical theorems, including those of Serre, Hurewicz, Blakers-Massey, and Whitehead; homotopy Sets; homotopy and homology decompositions of spaces and maps; and obstruction theory. The underlying theme of the entire book is the Eckmann-Hilton duality theory. It is assumed that the reader has had some exposure to the rudiments of homology theory and fundamental group theory. These topics are discussed in the appendices. The book can be used as a text for the second semester of an advanced ungraduate or graduate algebraic topology course. Carefully written treatment of a basic subject by a research worker in the field. Provides motivation with many illustrations and exercises. Exposition moves at a moderate pace, even in the later chapters. Differs from other texts on homotopy theory, in that the unifying theme of the entire book is the Eckmann-Hilton duality theory. Several appendices provide background information. INDICE: 1 Basic Homotopy. 2 H-Spaces and Co-H-Spaces. 3 Cofibrations and Fibrations. 4 Exact Sequences. 5 Applications of Exactness. 6 Homotopy Pushoutsand Pullbacks. 7 Homotopy and Homology Decompositions. 8 Homotopy Sets. 9 Obstruction Theory. A Point-Set Topology. B The Fundamental Group. C Homology andCohomology. D Homotopy Groups and the n-Sphere. E Homotopy Pushouts and Pullbacks. F Categories and Functors. Hints to Some of the Exercises. References. Index.-
- ISBN: 978-1-4419-7328-3
- Editorial: Springer
- Encuadernacion: Rústica
- Páginas: 344
- Fecha Publicación: 28/09/2011
- Nº Volúmenes: 1
- Idioma: Inglés