**Algebraic Topology**

by Allen Hatcher

**Publisher**: Cambridge University Press 2001**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

**The Geometry of Iterated Loop Spaces**

by

**J. P. May**-

**Springer**

A paper devoted to the study of iterated loop spaces. Our goal is to develop a simple and coherent theory which encompasses most of the known results about such spaces. We begin with some history and a description of the desiderata of such a theory.

(

**10287**views)

**Topology Illustrated**

by

**Peter Saveliev**-

**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.

(

**11314**views)

**Lectures on Introduction to Algebraic Topology**

by

**G. de Rham**-

**Tata Institute of Fundamental Research**

These notes were intended as a first introduction to algebraic Topology. Contents: Definition and general properties of the fundamental group; Free products of groups and their quotients; On calculation of fundamental groups; and more.

(

**9150**views)

**Algebraic and Geometric Surgery**

by

**Andrew Ranicki**-

**Oxford University Press**

Surgery theory is the standard method for the classification of high-dimensional manifolds, where high means 5 or more. This book aims to be an entry point to surgery theory for a reader who already has some background in topology.

(

**9697**views)