Invariant Forms on Grassmann Manifolds. (AM-89), Volume 89 / / Wilhelm Stoll.

• Superior document: Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
• VerfasserIn: Stoll, Wilhelm,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2016]; ©1978
• Year of Publication: 2016
• Language: English
• Series: Annals of Mathematics Studies ; 89
• Physical Description: 1 online resource (128 p.)

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 -- CONTENTS -- PREFACE -- GERMAN LETTERS -- INTRODUCTION -- 1. FLAG SPACES -- 2. SCHUBERT VARIETIES -- 3. CHERN FORMS -- 4. THE THEOREM OF BOTT AND CHERN -- 5. THE POINCARÉ DUAL OF A SCHUBERT VARIETY -- 6. MATSUSHIMA'S THEOREM -- 7. THE THEOREMS OF PIERI AND GIAMBELLI -- APPENDIX -- REFERENCES -- INDEX -- Backmatter