Algebraic Topology

Algebraic Topology

This free 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.

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.

Contents

  • Some Underlying Geometric Notions
  • The Fundamental Group
  • Homology
  • Cohomology
  • Homotopy Theory

Book Details

Author(s): Allen Hatcher
Publisher: Cambridge University Press
Format(s): PDF
File size: 3.57 MB
Number of pages: 559
Link: Download.







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