This book is the result of lecture courses on algebraic topology given by the author at the University of Manchester in 1967-1970,at Cornell University in 1970-1971 and at the Georg August University,Gottingen,in 1971-1972.The level of the material is more advanced than that of a first-year graduate course in algebraic topology;it is assumed that the student has already had a course on basic algebraic topology which included singular homology,the fundamental group and covering spaces.Moreover,a student who has never encountered differentiable manifolds will probably have difficulty with Chapter 12.On the other hand no knowledge of homotopy theory beyond the fundamental group is assumed.
Chapter 0 Some Facts from General Topology
Chapter 1 Categories,Functors and NaturalTransformations
Chapter 2 Homotopy Sets and Groups
Chapter 3 Properties of the Homotopy Groups
Chapter 4 Fibrations
Chapter 5 CW-Complexes
Chapter 6 Homotopy Properties of CW-Complexes
Chapter 7 Homology and Cohomology Theories
Chapter 8 Spectra
Chapter 9 Representation Theorems
Chapter 10 Ordinary Homology Theory
Chapter 11 Vector Bundles and K-Theory
Chapter 12 Manifolds and Bordism
Chapter 13 Products
Chapter 14 Orientation and Duality
Chapter 15 Spectral Sequences
Chapter 16 Characteristic Classes
Chapter 17 Cohomology Operations and Homology Cooperations
Chapter 18 The Steenrod Algebra and its Dual
Chapter 19 The Adams Spectral Sequence and the e-Invariant
Chapter 20 Calculation of the Cobordism Groups
Bibliography
Subject Index