Algebraic Topology

In most mathematics departments at major universities one of the three or four basic first-year graduate courses is in the subject of algebraic topology. This introductory textbook in algebraic topology is suitable for use in a course or for self-study featuring broad coverage of the subject and a readable exposition with many examples and exercises. The four main chapters present the basic material of the subject: fundamental group and covering spaces homology and cohomology higher homotopy groups and homotopy theory generally. The author emphasizes the geometric aspects of the subject which helps students gain intuition. A unique feature of the book is the inclusion of many optional topics which are not usually part of a first course due to time constraints and for which elementary expositions are sometimes hard to find. Among these are: Bockstein and transfer homomorphisms direct and inverse limits H-spaces and Hopf algebras the Brown representability theorem the James reduced product the Dold-Thom theorem and a full exposition of Steenrod squares and powers. Researchers will also welcome this aspect of the book. Language: English