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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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CR structures on open manifolds
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by Howard Jacobowitz and Peter Landweber PDF
Proc. Amer. Math. Soc. 144 (2016), 235-248 Request permission

Abstract:

We show that the vanishing of the higher dimensional homology groups of a manifold ensures that every almost CR structure of codimension $k$ may be homotoped to a CR structure. This result is proved by adapting a method Haefliger used to study foliations (and previously applied to study the relation between almost complex and complex structures on manifolds) to the case of (almost) CR structures on open manifolds.
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Additional Information
  • Howard Jacobowitz
  • Affiliation: Department of Mathematical Sciences, Rutgers University, Camden, New Jersey 08102
  • MR Author ID: 190037
  • Email: jacobowi@camden.rutgers.edu
  • Peter Landweber
  • Affiliation: Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854
  • MR Author ID: 109925
  • Email: landwebe@math.rutgers.edu
  • Received by editor(s): September 3, 2014
  • Received by editor(s) in revised form: December 12, 2014
  • Published electronically: April 14, 2015

  • Dedicated: Dedicated with admiration to André Haefliger
  • Communicated by: Franc Forstneric
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 235-248
  • MSC (2010): Primary 32V05; Secondary 55S35
  • DOI: https://doi.org/10.1090/proc/12700
  • MathSciNet review: 3415592