Invariant Forms on Grassmann Manifolds
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A01=Wilhelm Stoll
Author_Wilhelm Stoll
Calculation
Category=PBM
Category=PBV
Cohomology
Cohomology ring
Complex space
Cotangent bundle
Diagram (category theory)
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Exterior algebra
Grassmannian
Holomorphic vector bundle
Manifold
Regular map (graph theory)
Remainder
Representation theorem
Schubert variety
Sesquilinear form
Theorem
Vector bundle
Vector space
Product details
- ISBN 9780691081991
- Weight: 198g
- Dimensions: 152 x 229mm
- Publication Date: 21 Jan 1978
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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.
