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Top-Degree Global Solvability in CR and Locally Integrable Hypocomplex Structures

The Journal of Geometric Analysis volume 31, pages 8156–8172 (2021)Cite this article

Abstract

We study the top-degree cohomology for the \({\bar{\partial }_b}\) operator defined on a generic submanifold of the complex space as well as for the differential complex associated with a locally integrable structure \({\mathcal {V}}\) over a smooth manifold. The main assumptions are that \({\mathcal {V}}\) is hypocomplex and that the differential complex is locally solvable in degree one. One of the main tools is an adaptation of a sheaf theoretical argument due to Ramis–Ruget–Verdier.

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Notes

  1. This is a consequence of the well known “five-term exact sequence” associated to a first quadrant spectral sequence.

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Authors and Affiliations

  1. Institute of Mathematics and Statistics, University of São Paulo, São Paulo, SP, Brazil

    Paulo D. Cordaro

  2. Department of Mathematics, Federal University of São Carlos, São Carlos, SP, Brazil

    Max Reinhold Jahnke

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  1. Paulo D. Cordaro
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  2. Max Reinhold Jahnke
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Correspondence to Paulo D. Cordaro.

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During the development of this work, P. D. Cordaro was partially supported by FAPESP (2012/03168-7) and CNPq. M. R. Jahnke was supported by CNPq (process 140199/2014-4) and CAPES (PDSE 88881.131905/2016-01).

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Cordaro, P.D., Jahnke, M.R. Top-Degree Global Solvability in CR and Locally Integrable Hypocomplex Structures. J Geom Anal 31, 8156–8172 (2021). https://doi.org/10.1007/s12220-020-00573-1

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  • DOI: https://doi.org/10.1007/s12220-020-00573-1

Keywords

  • Tangential Cauchy-Riemann complexes
  • Hypocomplex manifolds
  • Top-degree cohomology

Mathematics Subject Classification

  • 35A01
  • 35G05
  • 32V05
  • 32V40