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Algebraic Topology

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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. I cannot prove it, but, I think many students go ga-ga for this book because so often Hatcher's style of proof is similar to that of an undergrad's: inconvenient details just "disappear" by the wayside if they're even brought up at all, and every other sentence features a leap in logic or an unremarked gap in reasoning that facilitates completion of an assignment by the deadline. We don’t share your credit card details with third-party sellers, and we don’t sell your information to others.

A unique feature is the inclusion of many optional topics not usually part of a first course due to time constraints: 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 Steenrod squares and powers.The electronic version has narrower margins than the print version for a better reading experience on portable electronic devices. In this book the authors present the technical tools needed for proving rigorously the classification theorem, give a detailed proof using these tools, and also discuss the history of the theorem and its various proofs. Some of the topics are: the shape of the universe, configuration spaces, digital image analysis, data analysis, social choice, and, of course, calculus. This is a reminder for me to go back and try simplifying the proof given the insight gained from the original.

A unique feature is the inclusion of many optional topics not usually part of a first course due to time constraints: 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 Steenrod squares and powers. To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies.A couple of notes from courses by Mike Hopkins on elliptic cohomology and related stuff: 1995, 1999.

Upon getting a hold of Rotman’s book (Massey’s is good too), the bunches of nontrivial examples made sense, expanding my knowledge. His beautiful concise course is a classic for good reason; we so rarely have an expert give us his "take" on a field.

Whether this is a good book or a bad book depends on your background, what you hope to gain from it, how much time you have, and (if your available time is not measured in years) how willing you are to take many things on faith as you press forward through homology, cohomology and homotopy theory. May is one of the Gods of the subject and anyone interested in topology owes it to themselves to read his papers and books. Both charges are true for a simple reason: Treating hard concepts with fluff prose is bound to frustrate the more analytical reader who insists on understanding each nut and bolt in a mechanism. It deals pretty early with spectral sequences and proves some standard results in classical homotopy theory via them (like Blakers-Massey, Freudenthal.

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