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Transactions of the American Mathematical Society

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On the cohomology groups of a polarisation and diagonal quantisation

Author: J. H. Rawnsley
Journal: Trans. Amer. Math. Soc. 230 (1977), 235-255
MSC: Primary 58A10; Secondary 58A30, 58F05, 81.58
MathSciNet review: 0648775
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Abstract: The sheaf $ {\mathcal{S}_F}(L)$ of germs of sections of a line bundle L on a manifold X covariant constant with respect to a flat connection defined for vectors in a complex subbundle F of the tangent bundle has a resolution by differential forms defined on F with values in L provided F satisfies the integrability conditions of the complex Frobenius theorem. This includes as special cases the de Rham and Dolbeault resolutions.

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Keywords: Line bundle, integrable tangent subbundle, sheaf of covariant constant sections, Poincaré lemma, resolution, periodic Hamiltonian flow, quantisation, Bohr-Sommerfeld condition
Article copyright: © Copyright 1977 American Mathematical Society

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