Cohomology Operations and Applications in Homotopy Theory (Dover Books on Mathematics) by Robert E. Mosher (PDF)

Description

Cohomology operations are at the center of a major area of activity in algebraic topology. This technique for supplementing and enriching the algebraic structure of the cohomology ring has been instrumental to important progress in general homotopy theory and in specific geometric applications. For both theoretical and practical reasons, the formal properties of families of operations have received extensive analysis.This text focuses on the single most important sort of operations, the Steenrod squares. It constructs these operations, proves their major properties, and provides numerous applications, including several different techniques of homotopy theory useful for computation. In the later chapters, the authors place special emphasis on calculations in the stable range. The text provides an introduction to methods of Serre, Toda, and Adams, and carries out some detailed computations. Prerequisites include a solid background in cohomology theory and some acquaintance with homotopy groups.

User’s Reviews

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

⭐This doesn’t make any sense, but somehow it’s a terrible book and yet I like it a lot. If you need to learn the stuff that’s in here, you don’t have a lot of choices. It is very difficult to find well-written mathematics at this level; I would recommend this as a “best of al evils.”

⭐This is a good book for those who understand advanced algebraic topology. It is simplified as much as possible. If you are beginning to learn about gadgets like Steenrod algebra and some of the related topics in Algebraic topology, nothing can be better than this.

⭐This is a great fast paced introduction to several structures in homotopy theory, by way of carefully explaining Steenrod Squares. You need to understand basic algebraic topology homology/cohomology/homotopy groups very well already, up to the point of obstruction theory and ideally Postnikov towers to take good advantage of what the book offers. The first chapter is an introduction to Eilenberg-MacLane spaces with a 1.5 page review of obstruction theory. The book is well written and pedagogical for the advanced student.

⭐I’ve already red many books and articles about Steenrod Operations but I never understood them. With this book all was clear, thank you very much sir Mosher

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