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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Complex-foliated structures. I. Cohomology of the Dolbeault-Kostant complexes


Authors: Hans R. Fischer and Floyd L. Williams
Journal: Trans. Amer. Math. Soc. 252 (1979), 163-195
MSC: Primary 58A30; Secondary 32L10, 58F06, 81C40
MathSciNet review: 534116
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Abstract: We study the cohomology of differential complexes, which we shall call Dolbeault-Kostant complexes, defined by certain integrable sub-bundles F of the complex tangent bundle of a manifold M. When M has a complex or symplectic structure and F 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 F insures that our complexes are elliptic. Assuming ellipticity and compactness of M, for example, one of our key results is a Hirzebruch-Riemann-Roch Theorem.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1979-0534116-X
PII: S 0002-9947(1979)0534116-X
Keywords: Sheaf cohomology, Chern class, Todd class, spectral sequence, elliptic complex
Article copyright: © Copyright 1979 American Mathematical Society