Logo

Algebraic Topology by Allen Hatcher

Large book cover: Algebraic Topology

Algebraic Topology
by

Publisher: Cambridge University Press
ISBN/ASIN: 0521795400
ISBN-13: 9780521795401
Number of pages: 560

Description:
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.

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

Similar books

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.
(9182 views)
Book cover: Topology IllustratedTopology Illustrated
by - Intelligent Perception
The text follows the content of a fairly typical, two-semester, first course in topology. Some of the topics are: the shape of the universe, configuration spaces, digital image analysis, data analysis, social choice, and, of course, calculus.
(11960 views)
Book cover: The Classification Theorem for Compact SurfacesThe Classification Theorem for Compact Surfaces
by
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.
(14699 views)
Book cover: Topology of Stratified SpacesTopology of Stratified Spaces
by - Cambridge University Press
This book concerns the study of singular spaces using techniques of geometry and topology and interactions among them. The authors cover intersection homology, L2 cohomology and differential operators, the topology of algebraic varieties, etc.
(8706 views)