Vector fields on Singular Varieties

• Main Authors: Brasselet, Jean-Paul (Author), Seade, José (Author), Suwa, Tatsuo (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Series: Lecture Notes in Mathematics, 1987
• Subjects: Mathematics.; Algebraic geometry.; Dynamics.; Ergodic theory.; Global analysis (Mathematics).; Manifolds (Mathematics).; Functions of complex variables.; Complex manifolds.; 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.

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, a...

Table of 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.