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- W2072289231 abstract "We study the cohomology of differential complexes, which we shall call Dolbeault-Kostant complexes, defined by certain integrable sub-bundles <italic>F</italic> of the complex tangent bundle of a manifold <italic>M</italic>. When <italic>M</italic> has a complex or symplectic structure and <italic>F</italic> is chosen to be the bundle of anti-holomorphic tangent vectors or, respectively, a “polarization” then the corresponding complexes are, respectively, the Dolbeault complex and (under further conditions) a complex introduced by Kostant in the context of geometric quantization. A simple condition on <italic>F</italic> insures that our complexes are elliptic. Assuming ellipticity and compactness of <italic>M</italic>, for example, one of our key results is a Hirzebruch-Riemann-Roch Theorem." @default.
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- W2072289231 date "1979-01-01" @default.
- W2072289231 modified "2023-09-26" @default.
- W2072289231 title "Complex-foliated structures. I. Cohomology of the Dolbeault-Kostant complexes" @default.
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- W2072289231 doi "https://doi.org/10.1090/s0002-9947-1979-0534116-x" @default.
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