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.
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评分Reread for Professor Maryam Mirzakhani - most attractive woman I've ever known.
评分這本超厚的書在今晚的考試和夜宵之後就會被放在書架上瞭。 我可能會忘記所有的代數拓撲的東西，但忘不掉這個令人感動的夜晚。
评分第四章就不讀瞭。。
评分關於homology的討論一上來就太具體瞭，如果先看過axioms再具體的homology會簡單很多。但是還是要給5星，因為無hatcher，無代數拓撲。
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