Invariant forms on Grassmann manifolds
Author(s)
Bibliographic Information
Invariant forms on Grassmann manifolds
（Annals of mathematics studies, no. 89）
Princeton University Press , University of Tokyo Press, 1977
- : pbk
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Note
Bibliography: p. 110-112
Includes index
Description and Table of Contents
- Volume
-
ISBN 9780691081984
Description
This work offers a contribution in the geometric form of the theory of several complex variables. Since complex Grassmann manifolds serve as classifying spaces of complex vector bundles, the cohomology structure of a complex Grassmann manifold is of importance for the construction of Chern classes of complex vector bundles. The cohomology ring of a Grassmannian is therefore of interest in topology, differential geometry, algebraic geometry, and complex analysis. Wilhelm Stoll treats certain aspects of the complex analysis point of view.
This work originated with questions in value distribution theory. Here analytic sets and differential forms rather than the corresponding homology and cohomology classes are considered. On the Grassmann manifold, the cohomology ring is isomorphic to the ring of differential forms invariant under the unitary group, and each cohomology class is determined by a family of analytic sets.
- Volume
-
: pbk ISBN 9780691081991
Description
This work offers a contribution in the geometric form of the theory of several complex variables. Since complex Grassmann manifolds serve as classifying spaces of complex vector bundles, the cohomology structure of a complex Grassmann manifold is of importance for the construction of Chern classes of complex vector bundles. The cohomology ring of a Grassmannian is therefore of interest in topology, differential geometry, algebraic geometry, and complex analysis. Wilhelm Stoll treats certain aspects of the complex analysis point of view. This work originated with questions in value distribution theory. Here analytic sets and differential forms rather than the corresponding homology and cohomology classes are considered. On the Grassmann manifold, the cohomology ring is isomorphic to the ring of differential forms invariant under the unitary group, and each cohomology class is determined by a family of analytic sets.
Table of Contents
*Frontmatter, pg. i*CONTENTS, pg. v*PREFACE, pg. vii*GERMAN LETTERS, pg. ix*INTRODUCTION, pg. 1*1. FLAG SPACES, pg. 11*2. SCHUBERT VARIETIES, pg. 27*3. CHERN FORMS, pg. 35*4. THE THEOREM OF BOTT AND CHERN, pg. 43*5. THE POINCARE DUAL OF A SCHUBERT VARIETY, pg. 57*6. MATSUSHIMA'S THEOREM, pg. 64*7. THE THEOREMS OF PIERI AND GIAMBELLI, pg. 82*APPENDIX, pg. 103*REFERENCES, pg. 110*INDEX, pg. 113*Backmatter, pg. 115
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