Endomorphisms of the Cohomology of Complex Grassmannians

DOI10.2307/2000083zbMath0566.14022OpenAlexW4249084759MaRDI QIDQ3680956

Michael E. Hoffman

Publication date: 1984

Full work available at URL: https://doi.org/10.2307/2000083

zbMATH Keywords

hard Lefschetz theoremcomplex Grassmannianendomorphisms of the rational cohomology algebra

Mathematics Subject Classification ID

Grassmannians, Schubert varieties, flag manifolds (14M15) Homology and cohomology of homogeneous spaces of Lie groups (57T15) Classification of mappings in algebraic topology (55S37)

Related Items

Relative Gottlieb groups of embeddings between complex Grassmannians ⋮ Filtering cohomology of ordinary and Lagrangian Grassmannians ⋮ Endomorphisms of real Grassmannians that commute with Steenrod squares ⋮ Cohomology algebra of mapping spaces between quaternion Grassmannians ⋮ Gröbner bases for (partial) flag manifolds ⋮ The degree of a Schubert variety. ⋮ On Lefschetz series ⋮ Rational homotopy of mapping spaces between complex Grassmannians ⋮ Maps between certain complex Grassmann manifolds ⋮ Rational cohomology algebra of mapping spaces between complex Grassmannians ⋮ Self-Maps of Loop Spaces. I ⋮ On Cohomology Automorphisms of Complex Flag Manifolds ⋮ Rationalized evaluation subgroups of mapping spaces between complex Grassmannians ⋮ Relative Gottlieb groups of the Pl\"ucker embedding of some complex Grassmanians ⋮ On self-maps of complex flag manifolds ⋮ Rigidity properties of compact Lie groups modulo maximal tori

Cites Work

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• On the genus of generalized flag manifolds
• Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts
• On the Relation of S -Functions to Schubert Varieties
• Rational Automorphisms of Grassmann Manifolds
• Homotopy Rigidity for Grassmannians
• Self-Maps of Flag Manifolds
• Rational homotopy theory and differential forms