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Transactions of the American Mathematical Society

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Dolbeault homotopy theory


Authors: Joseph Neisendorfer and Laurence Taylor
Journal: Trans. Amer. Math. Soc. 245 (1978), 183-210
MSC: Primary 32C10; Secondary 14F40, 55P62, 57R99, 58A14
DOI: https://doi.org/10.1090/S0002-9947-1978-0511405-5
MathSciNet review: 511405
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Abstract: For complex manifolds, we define ``complex homotopy groups'' in terms of the Dolbeault complex. Many theorems of classical homotopy theory are reflected in the properties of complex homotopy groups. Analytic fibre bundles yield long exact sequences of complex homotopy groups and various Hurewicz theorems relate complex homotopy groups to the Dolbeault cohomology. In a more analytic vein, the classical Fröhlicher spectral sequence has a complex homotopy analogue.

We compute these complex homotopy invariants for such examples as Calabi-Eckmann manifolds, Stein manifolds, and complete intersections.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1978-0511405-5
Keywords: Rational homotopy theory, Dolbeault cohomology, complex manifolds, Fröhlicher spectral sequence, Hurewicz theorem, Kahler manifold, Whitehead products
Article copyright: © Copyright 1978 American Mathematical Society

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