Fibre bundles play an important role in just about every aspect of modern geometry and topology. Basic properties, homotopy classification, and characteristic classes of fibre bundles have become an essential part of graduate mathematical education for students in geometry and mathematical physics. In this third edition two new chapters on the gauge group of a bundle and on the differential forms representing characteristic classes of complex vector bundles on manifolds have been added. These chapters result from the important role of the gauge group in mathematical physics and the continual usefulness of characteristic classes defined with connections on vector bundles.
For graduate mathematics students, explains the general theory of fiber bundles and their universal application to manifolds, the elements of K-theory, and the several characteristic classes. The third edition includes new chapters on the gauge group of a principal bundle, and the definition of Chern classes by differential forms; the second edition added a section on the Adams conjecture; first published in 1966. Annotation c. Book News, Inc., Portland, OR (booknews.com)