Algebraic Topology by Allen Hatcher

Large book cover: Algebraic Topology

Algebraic Topology

Publisher: Cambridge University Press
ISBN/ASIN: 0521795400
ISBN-13: 9780521795401
Number of pages: 559

In most major universities one of the three or four basic first-year graduate mathematics courses is algebraic topology. This introductory text is suitable for use in a course on the subject or for self-study, featuring broad coverage and a readable exposition, with many examples and exercises. The four main chapters present the basics: 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 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.

Home page url

Download or read it online for free here:
Download link
(3.5MB, PDF)

Similar books

Book cover: A Primer on Homotopy ColimitsA Primer on Homotopy Colimits
by - University of Oregon
This is an expository paper on homotopy colimits and homotopy limits. These are constructions which should arguably be in the toolkit of every modern algebraic topologist. Many proofs are avoided, or perhaps just sketched.
Book cover: Prerequisites in Algebraic TopologyPrerequisites in Algebraic Topology
by - NTNU
This is not an introductory textbook in algebraic topology, these notes attempt to give an overview of the parts of algebraic topology, and in particular homotopy theory, which are needed in order to appreciate that side of motivic homotopy theory.
Book cover: Homotopy Theories and Model CategoriesHomotopy Theories and Model Categories
by - University of Notre Dame
This paper is an introduction to the theory of model categories. The prerequisites needed for understanding this text are some familiarity with CW-complexes, chain complexes, and the basic terminology associated with categories.
Book cover: The Classification Theorem for Compact SurfacesThe Classification Theorem for Compact Surfaces
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.