Dolbeault Homotopy Theory

DOI10.2307/1998862zbMath0441.55014OpenAlexW4252398583MaRDI QIDQ3883171

Joseph A. Neisendorfer, Laurence R. Taylor

Publication date: 1978

Full work available at URL: https://doi.org/10.2307/1998862

zbMATH Keywords

formalityDolbeault complexKähler manifoldsCalabi-Eckmann manifoldsholomorphic p-formsanalytic fibre spacesantiholomorphic Hurewicz theoryantiholomorphic q-formscomplex homotopy invariantsDolbeault cohomotopy groupsDolbeault cohomotopy groups of an arbitrary Stein manifoldDolbeault homotopyEilenberg-Moore type spectral sequencesfree integral Whitehead algebras in the ordinary homotopy of complete intersectionsHodge decomposition of real homotopy typeholomorphic Hurewicz theoremsintegral Hurewicz homomorphism for a compact Kähler manifoldrational homotopy groups of complete intersectionsWhitehead coalgebra

Mathematics Subject Classification ID

Rational homotopy theory (55P62) Global differential geometry of Hermitian and Kählerian manifolds (53C55) Analytic sheaves and cohomology groups (32C35) Complete intersections (14M10) Complex manifolds (32Q99) Holomorphic bundles and generalizations (32L05) Eilenberg-Moore spectral sequences (55T20) Homotopy groups of special types (55Q70) Whitehead products and generalizations (55Q15) Cohomotopy groups (55Q55)

Related Items

Filtered 𝐴-infinity structures in complex geometry ⋮ Dolbeault and Bott-Chern formalities: deformations and \(\partial \overline{\partial}\)-lemma ⋮ Dolbeault-Massey triple products of low degree ⋮ Techniques of computations of Dolbeault cohomology of solvmanifolds ⋮ On cohomological and formal properties of strong Kähler with torsion and astheno-Kähler metrics ⋮ Formality of -objects ⋮ Transverse Kähler structures on central foliations of complex manifolds ⋮ On geometric Bott-Chern formality and deformations ⋮ Dolbeault cohomology of compact nilmanifolds ⋮ Higher-page Bott-Chern and Aeppli cohomologies and applications ⋮ Geometric formalities Along the Chern-Ricci flow ⋮ Quantitative and qualitative cohomological properties for non-Kähler manifolds ⋮ Remarks on Dolbeault cohomology of Oeljeklaus-Toma manifolds and Hodge theory ⋮ On the structure of double complexes ⋮ Compact nilmanifolds with nilpotent complex structures: Dolbeault cohomology ⋮ On Bott-Chern cohomology and formality ⋮ Dolbeault model and holomorphic fibre bundles

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