Invariant Forms on Grassmann Manifolds (Annals of Mathematics Studies, 89) - Hardcover

Stoll, Wilhelm

Hardcover

ISBN 10: 0691081980 ISBN 13: 9780691081984

Publisher: Princeton University Press, 1978

Synopsis

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.

About this title

From the Back Cover

Most of the results in this monograph are known. The method of proof is new, especially in the case of Matsushima's theorem. The topic is not easily accessible. Therefore an introduction has been written here in order to provide a clear, coherent, intransically formulated account which will be useful for applications to value distribution theory, and which may have a wider appeal as well.

Edition details

• Publisher: Princeton University Press
• Publication date: 1978
• Language: English
• ISBN 10: 0691081980
• ISBN 13: 9780691081984
• Binding: Hardcover
• Edition number: 1
• Number of pages: 128