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Geometry of characteristic classes
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Geometry of characteristic classes

Geometry of characteristic classes

Shigeyuki Morita

186 pages, parution le 01/01/1999

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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