Algebraic Topology

by Allen Hatcher


In most mathematics departments at major universities one of the three\nor four basic first-year graduate courses is in the subject of algebraic\ntopology. This introductory textbook in algebraic topology is suitable\nfor use in a course or for self-study, featuring broad coverage of\nthe subject and a readable exposition, with many examples and exercises.\nThe four main chapters present the basic material of the subject:\nfundamental group and covering spaces, homology and cohomology, higher\nhomotopy groups, and homotopy theory generally. The author emphasizes\nthe geometric aspects of the subject, which helps students gain intuition.\nA unique feature of the book is the inclusion of many optional topics\nwhich are not usually part of a first course due to time constraints,\nand for which elementary expositions are sometimes hard to find.\nAmong these are: Bockstein and transfer homomorphisms, direct and\ninverse limits, H-spaces and Hopf algebras, the Brown representability\ntheorem, the James reduced product, the Dold-Thom theorem, and a\nfull exposition of Steenrod squares and powers. Researchers will\nalso welcome this aspect of the book.

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