Topology, Geometry and Gauge fields: Interactions [Paperback]

A study of topology and geometry, beginning with a comprehensible account of the extraordinary and rather mysterious impact of mathematical physics, and especially gauge theory, on the study of the geometry and topology of manifolds. The focus of the book is the Yang-Mills-Higgs field and some considerable effort is expended to make clear its origin and significance in physics. Much of the mathematics developed here to study these fields is standard, but the treatment always keeps one eye on the physics and sacrifices generality in favor of clarity. The author brings readers up the level of physics and mathematics needed to conclude with a brief discussion of the Seiberg-Witten invariants. A large number of exercises are included to encourage active participation on the part of the reader.

Now in its second edition, this study of topology and geometry focuses on the Yang-Mills field and includes an account of the extraordinary impact of mathematical physics, and especially gauge theory, on the study of the geometry and topology of manifolds.

From the reviews:

MATHEMATICAL REVIEWS

The presentation in the remaining five chapters is enriched by detailed discussions about the physical interpretations of connections, their curves and characteristic classes. I particularly enjoyed Chapter 2 where many fundamental physical examples are discussed at great length in a reader friendly fashion. No detail is left to the readers imagination or interpretation. I am not aware of another source where these very important examples and ideas are presented at a level accessible to beginners&The topics covered in this book can be found in many other sources, but the presenl�