Invariant Forms on Grassmann Manifolds. (AM-89), Volume 89 (eBook)

Wilhelm Stoll (Autor)

eBook Download: PDF

2016 | 1. Auflage
128 Seiten
Princeton University Press (Verlag)
978-1-4008-8188-8 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 2.3.2016
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Annals of Mathematics Studies
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Graphentheorie
• Schlagworte: Calculation • cohomology • Cohomology ring • Complex Space • cotangent bundle • Diagram (category theory) • Exterior algebra • Grassmannian • Holomorphic vector bundle • manifold • Regular map (graph theory) • remainder • representation theorem • Schubert variety • Sesquilinear form • Theorem • vector bundle • Vector Space
• ISBN-10: 1-4008-8188-9 / 1400881889
• ISBN-13: 978-1-4008-8188-8 / 9781400881888