1.

Record Nr.

UNINA9910483981803321

Autore

Brasselet Jean-Paul

Titolo

Vector fields on Singular Varieties [[electronic resource] /] / by Jean-Paul Brasselet, José Seade, Tatsuo Suwa

Pubbl/distr/stampa

Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2009

ISBN

3-642-05205-3

Edizione

[1st ed. 2009.]

Descrizione fisica

1 online resource (XX, 232 p.)

Collana

Lecture Notes in Mathematics, , 0075-8434 ; ; 1987

Disciplina

515.94

Soggetti

Functions of complex variables

Dynamics

Ergodic theory

Manifolds (Mathematics)

Complex manifolds

Global analysis (Mathematics)

Algebraic geometry

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

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

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.

Sommario/riassunto

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.