Geometry of Characteristic Classes (Translations of Mathematical Monographs) - Softcover

American Mathematical Society

Softcover

ISBN 10: 0821821393 ISBN 13: 9780821821398

Publisher: American Mathematical Society, 2001

Synopsis

Characteristic classes are central to the modern study of the topology and geometry of manifolds. They were first introduced in topology, where, for instance, they could be used to define obstructions to the existence of certain fiber bundles. Characteristic classes were later defined (via the Chern-Weil theory) using connections on vector bundles, thus revealing their geometric side. In the late 1960s new theories arose that described still finer structures.Examples of the so-called secondary characteristic classes came from Chern-Simons invariants, Gelfand-Fuks cohomology, and the characteristic classes of flat bundles. The new techniques are particularly useful for the study of fiber bundles whose structure groups are not finite dimensional. The theory of characteristic classes of surface bundles is perhaps the most developed. Here the special geometry of surfaces allows one to connect this theory to the theory of moduli space of Riemann surfaces, i.e., Teichmuller theory. In this book Morita presents an introduction to the modern theories of characteristic classes.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2001
• Language: English
• ISBN 10: 0821821393
• ISBN 13: 9780821821398
• Binding: Paperback
• Number of pages: 185