Geometry of Characteristic Classes
About this Title
Shigeyuki Morita, Tokyo Institute of Technology, Tokyo, Japan
Publication: Translations of Mathematical Monographs
Publication Year: 2001; Volume 199
ISBNs: 978-0-8218-2139-8 (print); 978-1-4704-4625-3 (online)
MathSciNet review: MR1826571
MSC: Primary 57R20; Secondary 20F38, 32G15, 55P62, 55R40, 57R32
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 using connections on vector bundles, thus revealing their geometric side.
The purpose of this book is to introduce the reader to the three theories of characteristic classes that were developed in the late 1960s. They include characteristic classes of flat bundles, characteristic classes of foliations, and characteristic classes of surface bundles.
The book is intended for graduate students and research mathematicians working in various areas of geometry and topology.
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