Homology Theory

1. Front Matter

   Pages i-xiv

   PDF

2. Singular Homology Theory

   • James W. Vick

   Pages 1-34

3. Attaching Spaces with Maps

   • James W. Vick

   Pages 35-64

4. The Eilenberg—Steenrod Axioms

   • James W. Vick

   Pages 65-84

5. Covering Spaces

   • James W. Vick

   Pages 85-119

6. Products

   • James W. Vick

   Pages 120-142

7. Manifolds and Poincaré Duality

   • James W. Vick

   Pages 143-185

8. Fixed-Point Theory

   • James W. Vick

   Pages 186-210

9. Back Matter

   Pages 211-245

   PDF

The 20 years since the publication of this book have been an era of continuing growth and development in the field of algebraic topology. New generations of young mathematicians have been trained, and classical problems have been solved, particularly through the application of geometry and knot theory. Diverse new resources for introductory coursework have appeared, but there is persistent interest in an intuitive treatment of the basic ideas. This second edition has been expanded through the addition of a chapter on covering spaces. By analysis of the lifting problem it introduces the funda­ mental group and explores its properties, including Van Kampen's Theorem and the relationship with the first homology group. It has been inserted after the third chapter since it uses some definitions and results included prior to that point. However, much of the material is directly accessible from the same background as Chapter 1, so there would be some flexibility in how these topics are integrated into a course. The Bibliography has been supplemented by the addition of selected books and historical articles that have appeared since 1973.

• Algebraic topology
• CW complex
• cohomology
• fixed point theory
• homology
• point set topology
• set

• Department of Mathematics, The University of Texas at Austin, Austin, USA

  James W. Vick

Policies and ethics