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035   $a(DE-B1597)468003
035   $a(OCoLC)979633759
035   $a(DE-B1597)9781400881888
035   $a(EXLCZ)993710000000620151
100   $a20190708d2016      fg              
101 0 $aeng
135   $aurcnu||||||||
181   $2rdacontent
182   $2rdamedia
183   $2rdacarrier
200 10$aInvariant Forms on Grassmann Manifolds. (AM-89), Volume 89 /$fWilhelm Stoll
210  1$aPrinceton, NJ : $cPrinceton University Press, $d[2016]
210  4$d©1978
215   $a1 online resource (128 pages)
225 0 $aAnnals of Mathematics Studies ;$v252
311   $a0-691-08198-0 
311   $a0-691-08199-9 
320   $aIncludes bibliographical references and index.
327   $tFrontmatter -- $tCONTENTS -- $tPREFACE -- $tGERMAN LETTERS -- $tINTRODUCTION -- $t1. FLAG SPACES -- $t2. SCHUBERT VARIETIES -- $t3. CHERN FORMS -- $t4. THE THEOREM OF BOTT AND CHERN -- $t5. THE POINCARÉ DUAL OF A SCHUBERT VARIETY -- $t6. MATSUSHIMA'S THEOREM -- $t7. THE THEOREMS OF PIERI AND GIAMBELLI -- $tAPPENDIX -- $tREFERENCES -- $tINDEX -- $tBackmatter
330   $aThis work offers a contribution in the geometric form of the theory of several complex variables. Since complex Grassmann manifolds serve as classifying spaces of complex vector bundles, the cohomology structure of a complex Grassmann manifold is of importance for the construction of Chern classes of complex vector bundles. The cohomology ring of a Grassmannian is therefore of interest in topology, differential geometry, algebraic geometry, and complex analysis. Wilhelm Stoll treats certain aspects of the complex analysis point of view.This work originated with questions in value distribution theory. Here analytic sets and differential forms rather than the corresponding homology and cohomology classes are considered. On the Grassmann manifold, the cohomology ring is isomorphic to the ring of differential forms invariant under the unitary group, and each cohomology class is determined by a family of analytic sets.
410  0$aAnnals of mathematics studies ;$vNumber 89.
606   $aGrassmann manifolds
606   $aDifferential forms
606   $aInvariants
610   $aCalculation.
610   $aCohomology ring.
610   $aCohomology.
610   $aComplex space.
610   $aCotangent bundle.
610   $aDiagram (category theory).
610   $aExterior algebra.
610   $aGrassmannian.
610   $aHolomorphic vector bundle.
610   $aManifold.
610   $aRegular map (graph theory).
610   $aRemainder.
610   $aRepresentation theorem.
610   $aSchubert variety.
610   $aSesquilinear form.
610   $aTheorem.
610   $aVector bundle.
610   $aVector space.
615  0$aGrassmann manifolds.
615  0$aDifferential forms.
615  0$aInvariants.
676   $a514/.224
700   $aStoll$b Wilhelm, $0354798
801  0$bDE-B1597
801  1$bDE-B1597
906   $aBOOK
912   $a9910154752103321
996   $aInvariant Forms on Grassmann Manifolds. (AM-89), Volume 89$92788684
997   $aUNINA