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CR structures on open manifolds

Authors: Howard Jacobowitz and Peter Landweber
Journal: Proc. Amer. Math. Soc. 144 (2016), 235-248
MSC (2010): Primary 32V05; Secondary 55S35
Published electronically: April 14, 2015
MathSciNet review: 3415592
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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

Peter Landweber
Affiliation: Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854

Keywords: Almost complex, almost CR, Haefliger structure, Gromov's h-principle
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
Article copyright: © Copyright 2015 American Mathematical Society