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Título del libro: Vector Fields On Singular Varieties
Título del capítulo: The Case of Manifolds

Autores UNAM:
JOSE ANTONIO SEADE KURI;
Autores externos:
Idioma:
Inglés
Año de publicación:
2009
Resumen:

In this chapter we review briefly some of the fundamental results of the classical theory of indices of vector fields and characteristic classes of smooth manifolds. These were first defined in terms of obstructions to the construction of vector fields and frames. In the case of a vector field the Poincare-Hopf Theorem says that Euler-Poincare characteristic is the obstruction to constructing a nonzero vector field tangent to a compact manifold. Extension of this result to frames yields to the definition of Chern classes from the viewpoint of obstruction theory. There is another important point of view for defining characteristic classes on the differential geometry side, this is the Chern-Weil theory. Sections :3 and 4 provide an introduction to that theory and the corresponding definition of Chern classes. Finally, Sect. 5 sets up one of the key, features of this monograph: the interplay between localization via obstruction theory, which yields to the classical relative characteristi

Entidades citadas de la UNAM:
Fuente:



ISBN:
9783642052040
Editorial:
SPRINGER-VERLAG BERLIN

Tipo de producto:
Article



DOI:
10.1007/978-3-642-05205-7_1