Bibliographic Information

Geometry of characteristic classes

Shigeyuki Morita

(Translations of mathematical monographs, v. 199)(Iwanami series in modern mathematics)

American Mathematical Society, c2001

Other Title

特性類と幾何学

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Note

Includes bibliographical references (p. 179-182) and index

Description and Table of Contents

Description

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.

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.

by "Nielsen BookData"

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Details
  • NCID
    BA51790414
  • ISBN
    • 0821821393
  • LCCN
    00054312
  • Country Code
    us
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Original Language Code
    jpn
  • Place of Publication
    Providence, R.I.
  • Pages/Volumes
    xiii, 185 p.
  • Size
    22 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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