Tatsuo Suwa's Books

Complex Analytic Geometry: From The Localization Viewpoint

By: Tatsuo Suwa

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Complex Analytic Geometry: From The Localization Viewpoint

By: Tatsuo Suwa

Complex Analytic Geometry is a subject that could be termed, in short, as the study of the sets of common zeros of complex analytic functions. It has a long history and is closely related to many other fields of Mathematics and Sciences, where numerous applications have been found, including a recent one in the Sato hyperfunction theory.This book is concerned with, among others, local invariants that arise naturally in Complex Analytic Geometry and their relations with global invariants of the manifold or variety. The idea is to look at them as residues associated with the localization of some characteristic classes. Two approaches are taken for this — topological and differential geometric — and the combination of the two brings out further fruitful results. For this, on one hand, we present detailed description of the Alexander duality in combinatorial topology. On the other hand, we give a thorough presentation of the Čech-de Rham cohomology and integration theory on it. This viewpoint provides us with the way for clearer and more precise presentations of the central concepts as well as fundamental and important results that have been treated only globally so far. It also brings new perspectives into the subject and leads to further results and applications.The book starts off with basic material and continues by introducing characteristic classes via both the obstruction theory and the Chern-Weil theory, explaining the idea of localization of characteristic classes and presenting the aforementioned invariants and relations in a unified way from this perspective. Various related topics are also discussed. The expositions are carried out in a self-containing manner and includes recent developments. The profound consequences of this subject will make the book useful for students and researchers in fields as diverse as Algebraic Geometry, Complex Analytic Geometry, Differential Geometry, Topology, Singularity Theory, Complex Dynamical Systems, Algebraic Analysis and Mathematical Physics.

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Page Count

609

Publisher

World Scientific

Published Date

ISBN 10

9814704296

ISBN 13

9789814704298

Vector Fields on Singular Varieties

By: Jean-Paul Brasselet,José Seade,Tatsuo Suwa

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Vector Fields on Singular Varieties

By: Jean-Paul Brasselet,José Seade,Tatsuo Suwa

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.

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Page Count

242

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642052045

ISBN 13

9783642052040

Complex Analytic Geometry: From The Localization Viewpoint

By: Tatsuo Suwa

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Complex Analytic Geometry: From The Localization Viewpoint

By: Tatsuo Suwa

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N/A

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Solve jigsaw puzzle

Age

Page Count

609

Publisher

World Scientific

Published Date

ISBN 10

9814704296

ISBN 13

9789814704298

Vector Fields on Singular Varieties

By: Jean-Paul Brasselet,José Seade,Tatsuo Suwa

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Vector Fields on Singular Varieties

By: Jean-Paul Brasselet,José Seade,Tatsuo Suwa

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N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

242

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642052045

ISBN 13

9783642052040

Book's by Tatsuo Suwa

Complex Analytic Geometry: From The Localization Viewpoint

Complex Analytic Geometry: From The Localization Viewpoint

Vector Fields on Singular Varieties

Vector Fields on Singular Varieties

Complex Analytic Geometry: From The Localization Viewpoint

Complex Analytic Geometry: From The Localization Viewpoint

Vector Fields on Singular Varieties

Vector Fields on Singular Varieties

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