Table of Contents

Preface 1. Basic Notions of Topology and the Value of Topological Reasoning 2. Differential Geometry: Manifolds and Differential Forms 3. The Fundamental Group 4. The Homology Groups 5. The Higher Homotopy Groups 6. Cohomology and De Rhan Cohomology 7. Fibre Bundles and Further Differential Geometry 8. Morse Theory 9. Defects, Textures, and NHomotopy Theory 10. Yang-Mills Theories: Instantons and Monopoles Further Reading Subject Index

About the Author

Charles Nash is a Professor of Mathematics at the National University of Ireland. His main research interests are quantum field theory and differential topology.
Siddhartha Sen is Professor Emeritus in Applied Mathematics at the University College of Dublin.