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On the cohomology groups of holomorphic Banach bundles


Author: László Lempert
Journal: Trans. Amer. Math. Soc. 361 (2009), 4013-4025
MSC (2000): Primary 32L05, 32L10, 58B15
DOI: https://doi.org/10.1090/S0002-9947-09-04835-1
Published electronically: March 12, 2009
MathSciNet review: 2500876
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Abstract: We consider a compact complex manifold $ M$ and introduce the notion of two holomorphic Banach bundles $ E,F$ over $ M$ being compact perturbations of one another. Given two such bundles we show that if the cohomology groups $ H^{q}(M,E)$ are finite dimensional, then so are the cohomology groups $ H^{q}(M,F)$; as well as a more precise result in the same spirit.


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Additional Information

László Lempert
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395

DOI: https://doi.org/10.1090/S0002-9947-09-04835-1
Received by editor(s): May 4, 2007
Published electronically: March 12, 2009
Additional Notes: This research was partially supported by NSF grants DMS0203072 and 0700281
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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