Vector fields on Singular Varieties / by Jean-Paul Brasselet, José Seade, Tatsuo Suwa.

Format:

Book

Author/Creator:

Brasselet, Jean-Paul, author.

Seade, José, author.

Suwa, T. (Tatsuo), 1942- author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1987.

Lecture Notes in Mathematics, 0075-8434 ; 1987

Language:

English

Subjects (All):

Differential equations, Partial.

Differentiable dynamical systems.

Cell aggregation--Mathematics.

Cell aggregation.

Global analysis (Mathematics).

Geometry, Algebraic.

Several Complex Variables and Analytic Spaces.

Dynamical Systems and Ergodic Theory.

Manifolds and Cell Complexes (incl. Diff.Topology).

Global Analysis and Analysis on Manifolds.

Algebraic Geometry.

Local Subjects:

Several Complex Variables and Analytic Spaces.

Dynamical Systems and Ergodic Theory.

Manifolds and Cell Complexes (incl. Diff.Topology).

Global Analysis and Analysis on Manifolds.

Algebraic Geometry.

Physical Description:

1 online resource (XX, 232 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.

System Details:

text file PDF

Summary:

Vector fields on manifolds play a major role in mathematics and other sciences. In particular, the Poincaré-Hopf index theorem gives rise to the theory of Chern classes, key manifold-invariants in geometry and topology. It is natural to ask what is the 'good' notion of the index of a vector field, and of Chern classes, if the underlying space becomes singular. The question has been explored by several authors resulting in various answers, starting with the pioneering work of M.-H. Schwartz and R. MacPherson. We present these notions in the framework of the obstruction theory and the Chern-Weil theory. The interplay between these two methods is one of the main features of the monograph.

Contents:

The Case of Manifolds

The Schwartz Index

The GSV Index

Indices of Vector Fields on Real Analytic Varieties

The Virtual Index

The Case of Holomorphic Vector Fields

The Homological Index and Algebraic Formulas

The Local Euler Obstruction

Indices for 1-Forms

The Schwartz Classes

The Virtual Classes

Milnor Number and Milnor Classes

Characteristic Classes of Coherent Sheaves on Singular Varieties.

Other Format:

Printed edition:

ISBN:

9783642052057

Access Restriction:

Restricted for use by site license.