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- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 1987)
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Table of contents (13 chapters)
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Front Matter
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Back Matter
About this book
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.
Reviews
From the reviews:
“This book is dedicated to the study of indices of vector fields and flows around an isolated singularity, or stationary point, in the cases where the underlying space is either a manifold or a singular variety. … The book gives a thorough presentation of the results, old and new, related to indices of vector fields on singular varieties and is a valuable reference for both the specialist and the non-specialist.” (M. G. Soares, Mathematical Reviews, Issue 2011 d)Authors and Affiliations
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Inst. de Mathématiques de Luminy (IML), CNRS , Marseille Cedex 9, France
Jean-Paul Brasselet
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Instituto de Matématicas, Universidad Nacional Autónomia, Cuernavaca, Morelos, Mexico
José Seade
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Dept. Mathematics, Hokkaido University, Sapporo, Hokkaido, Japan
Tatsuo Suwa
Bibliographic Information
Book Title: Vector fields on Singular Varieties
Authors: Jean-Paul Brasselet, José Seade, Tatsuo Suwa
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-642-05205-7
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2009
Softcover ISBN: 978-3-642-05204-0Published: 17 December 2009
eBook ISBN: 978-3-642-05205-7Published: 28 November 2009
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XX, 232
Topics: 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