Résumé
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., Teichmüller theory. In this book Morita presents an introduction to the modern theories of characteristic classes.
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
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | American Mathematical Society (AMS) |
| Auteur(s) | Shigeyuki Morita |
| Parution | 01/01/1999 |
| Nb. de pages | 186 |
| Format | 14 x 21,5 |
| Couverture | Broché |
| Poids | 235g |
| Intérieur | Noir et Blanc |
| EAN13 | 9780821821398 |
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