Algebraic Topology by Robert M. Switzer (PDF)

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From the reviews: “The author has attempted an ambitious and most commendable project. […] The book contains much material that has not previously appeared in this format. The writing is clean and clear and the exposition is well motivated. […] This book is, all in all, a very admirable work and a valuable addition to the literature.” Mathematical Reviews

User’s Reviews

Editorial Reviews: Review From the reviews:”This book contains much impressive mathematics, namely the achievements by algebraic topologists in obtaining extensive information on the stable homotopy groups of spheres, and the computation of various cobordism groups. It is a long book, and for the major part a very advanced book. … (It is) suitable for specialists, or for those who already know what algebraic topology is for, and want a guide to the principal methods of stable homotopy theory.”R. Brown in Bulletin of the London Mathematical Society, 1980″In the more than twenty five years since its first appearance, the book has met with favorable response, both in its use as a text and as reference. It is a good course which leads the reader systematically to the point at which he can begin to tackle problems in algebraic topology. … This book remains one of the best sources for the material which every young algebraic topologist should know.” (Corina Mohorianu, Zentralblatt MATH, Vol. 1003 (3), 2003) About the Author Biography of Robert M. SwitzerRobert M. Switzer was born in Tennessee (USA) in 1940.After majoring in mathematics at Harvard College, he completed his PhD at Stanford University in 1965. He spent 5 years as lecturer at the University of Manchester, England, and then moved to Goettingen, Germany, where he has been Professor of Mathematics since 1973. In the early 1980s his research concentrated on obstruction theory in connection with holomorphic bundles on projective spaces. In 1984 he switched his attention to Computer Science and has been teaching and working in that field ever since.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book was used for a second year graduate course in topology, and definitely is good at bridging the gaps between a first-year graduate course and higher-level subjects. That said, while this is self contained, it is not good for the first time you are reading the subject, pick up Hatcher or Bredon for that. I point out that acts more as a survey of the important materials, rather than an indepth introduction.

⭐best in depth introduction

⭐The earlier chapters are quite good; however, some of the advanced topics in this book are better approached (appreciated) after one has learned about them elsewhere, at a more leisurely pace. For instance, this isn’t the best place to first read about characteristic classes and topological K theory (I would recommend, without much hesitation, the books by Atiyah and Milnor & Stasheff, instead). Much to my disappointment, the chapter on spectral sequences is quite convoluted. Parts of ‘user’s guide’ by Mcleary would certainly come in handy here (which sets the stage rather nicely for applications).So it turns out that supplemental reading (exluding Whitehead’s massive treatise) is necessary to achieve a better understanding of algebraic topology at the level of this book. The homotopical view therein will be matched (possibly superseded) by Aguilar’s book (forthcoming, to which I am very much looking forward).Good luck!

⭐I can’t remember, if I ever bought a book a second time for myself. It’s definitely the first math book I’m rebuying, because my first Switzer is showing loads of wear after about 6 years of very regular use now. Every student, who wants to take Algebraic Topology seriously, is sure to return to this book regularly. In all honesty it should not be taken as a course in AT, since that would take ages. But it is a very good way to find almost all the details of “classical” knowledge contained in one place. Sadly it predates operads, the modern stable categories, the revival of model categories, and quite a few other things, still I don’t want to miss this jewel ever 🙂 Even after years I’m occasionally stunned, when a person tells me that something is in Switzer as well (most recently Bott periodicity).

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