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Transactions of the American Mathematical Society

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On 5-manifolds admitting rank two distributions of Cartan type


Authors: Shantanu Dave and Stefan Haller
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 58A30; Secondary 58J20, 53A40, 53C23, 53C27
DOI: https://doi.org/10.1090/tran/7495
Published electronically: September 6, 2018
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Abstract: We consider the question whether an orientable $ 5$-manifold can be equipped with a rank two distribution of Cartan type and what $ 2$-plane bundles can be realized. We obtain a complete answer for open manifolds. In the closed case, we settle the topological part of this problem and present partial results concerning its geometric aspects and new examples.


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Additional Information

Shantanu Dave
Affiliation: Wolfgang Pauli Institute c/o Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
Email: shantanu.dave@univie.ac.at

Stefan Haller
Affiliation: Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany
Address at time of publication: Department of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
Email: stefan.haller@univie.ac.at

DOI: https://doi.org/10.1090/tran/7495
Keywords: Rank two distributions of Cartan type in dimension five, parabolic geometry, h-principle, mod 2 index, Lutz--Martinez theorem
Received by editor(s): May 18, 2017
Received by editor(s) in revised form: December 14, 2017
Published electronically: September 6, 2018
Additional Notes: The first author was supported by the Austrian Sciences Fund (FWF) grant P24420.
Article copyright: © Copyright 2018 American Mathematical Society

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