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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Complex-foliated structures. I. Cohomology of the Dolbeault-Kostant complexes
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by Hans R. Fischer and Floyd L. Williams PDF
Trans. Amer. Math. Soc. 252 (1979), 163-195 Request permission

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
  • © Copyright 1979 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 252 (1979), 163-195
  • MSC: Primary 58A30; Secondary 32L10, 58F06, 81C40
  • DOI: https://doi.org/10.1090/S0002-9947-1979-0534116-X
  • MathSciNet review: 534116