Translations of Mathematical Monographs Iwanami Series in Modern Mathematics 2001; 185 pp; softcover Volume: 199 ISBN10: 0821821393 ISBN13: 9780821821398 List Price: US$43 Member Price: US$34.40 Order Code: MMONO/199
 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 ChernWeil 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 socalled secondary characteristic classes came from ChernSimons invariants, GelfandFuks 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., Teichmüller theory. In this book Morita presents an introduction to the modern theories of characteristic classes. Readership Graduate students and research mathematicians working in geometry. Table of Contents  De Rham homotopy theory
 Characteristic classes of flat bundles
 Characteristic classes of foliations
 Characteristic classes of surface bundles
 Directions and problems for future research
 Bibliography
 Index
